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Timoshenko beam theory</title> <meta name="description" content="Search results for: Nonlocal Timoshenko beam theory"> <meta name="keywords" content="Nonlocal Timoshenko beam theory"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> 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action="https://publications.waset.org/abstracts/search"> <div id="custom-search-input"> <div class="input-group"> <i class="fas fa-search"></i> <input type="text" class="search-query" name="q" placeholder="Author, Title, Abstract, Keywords" value="Nonlocal Timoshenko beam theory"> <input type="submit" class="btn_search" value="Search"> </div> </div> </form> </div> </div> <div class="row mt-3"> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Commenced</strong> in January 2007</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Frequency:</strong> Monthly</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Edition:</strong> International</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Paper Count:</strong> 5563</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: Nonlocal Timoshenko beam theory</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5563</span> Vibration Behavior of Nanoparticle Delivery in a Single-Walled Carbon Nanotube Using Nonlocal Timoshenko Beam Theory</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Haw-Long%20Lee">Haw-Long Lee</a>, <a href="https://publications.waset.org/abstracts/search?q=Win-Jin%20Chang"> Win-Jin Chang</a>, <a href="https://publications.waset.org/abstracts/search?q=Yu-Ching%20Yang"> Yu-Ching Yang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In the paper, the coupled equation of motion for the dynamic displacement of a fullerene moving in a (10,10) single-walled carbon nanotube (SWCNT) is derived using nonlocal Timoshenko beam theory, including the effects of rotary inertia and shear deformation. The effects of confined stiffness between the fullerene and nanotube, foundation stiffness, and nonlocal parameter on the dynamic behavior are analyzed using the Runge-Kutta Method. The numerical solution is in agreement with the analytical result for the special case. The numerical results show that increasing the confined stiffness and foundation stiffness decrease the dynamic displacement of SWCNT. However, the dynamic displacement increases with increasing the nonlocal parameter. In addition, result using the Euler beam theory and the Timoshenko beam theory are compared. It can be found that ignoring the effects of rotary inertia and shear deformation leads to an underestimation of the displacement. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=single-walled%20carbon%20nanotube" title="single-walled carbon nanotube">single-walled carbon nanotube</a>, <a href="https://publications.waset.org/abstracts/search?q=nanoparticle%20delivery" title=" nanoparticle delivery"> nanoparticle delivery</a>, <a href="https://publications.waset.org/abstracts/search?q=Nonlocal%20Timoshenko%20beam%20theory" title=" Nonlocal Timoshenko beam theory"> Nonlocal Timoshenko beam theory</a>, <a href="https://publications.waset.org/abstracts/search?q=Runge-Kutta%20Method" title=" Runge-Kutta Method"> Runge-Kutta Method</a>, <a href="https://publications.waset.org/abstracts/search?q=Van%20der%20Waals%20force" title=" Van der Waals force"> Van der Waals force</a> </p> <a href="https://publications.waset.org/abstracts/65037/vibration-behavior-of-nanoparticle-delivery-in-a-single-walled-carbon-nanotube-using-nonlocal-timoshenko-beam-theory" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/65037.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">377</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5562</span> Nonlocal Beam Models for Free Vibration Analysis of Double-Walled Carbon Nanotubes with Various End Supports</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Babak%20Safaei">Babak Safaei</a>, <a href="https://publications.waset.org/abstracts/search?q=Ahmad%20Ghanbari"> Ahmad Ghanbari</a>, <a href="https://publications.waset.org/abstracts/search?q=Arash%20Rahmani"> Arash Rahmani</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In the present study, the free vibration characteristics of double-walled carbon nanotubes (DWCNTs) are investigated. The small-scale effects are taken into account using the Eringen’s nonlocal elasticity theory. The nonlocal elasticity equations are implemented into the different classical beam theories namely as Euler-Bernoulli beam theory (EBT), Timoshenko beam theory (TBT), Reddy beam theory (RBT), and Levinson beam theory (LBT) to analyze the free vibrations of DWCNTs in which each wall of the nanotubes is considered as individual beam with van der Waals interaction forces. Generalized differential quadrature (GDQ) method is utilized to discretize the governing differential equations of each nonlocal beam model along with four commonly used boundary conditions. Then molecular dynamics (MD) simulation is performed for a series of armchair and zigzag DWCNTs with different aspect ratios and boundary conditions, the results of which are matched with those of nonlocal beam models to extract the appropriate values of the nonlocal parameter corresponding to each type of chirality, nonlocal beam model and boundary condition. It is found that the present nonlocal beam models with their proposed correct values of nonlocal parameter have good capability to predict the vibrational behavior of DWCNTs, especially for higher aspect ratios. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=double-walled%20carbon%20nanotubes" title="double-walled carbon nanotubes">double-walled carbon nanotubes</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlocal%20continuum%20elasticity" title=" nonlocal continuum elasticity"> nonlocal continuum elasticity</a>, <a href="https://publications.waset.org/abstracts/search?q=free%20vibrations" title=" free vibrations"> free vibrations</a>, <a href="https://publications.waset.org/abstracts/search?q=molecular%20dynamics%20simulation" title=" molecular dynamics simulation"> molecular dynamics simulation</a>, <a href="https://publications.waset.org/abstracts/search?q=generalized%20differential%20quadrature%20method" title=" generalized differential quadrature method"> generalized differential quadrature method</a> </p> <a href="https://publications.waset.org/abstracts/41557/nonlocal-beam-models-for-free-vibration-analysis-of-double-walled-carbon-nanotubes-with-various-end-supports" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/41557.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">294</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5561</span> Vibration of Nonhomogeneous Timoshenko Nanobeam Resting on Winkler-Pasternak Foundation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Somnath%20Karmakar">Somnath Karmakar</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20Chakraverty"> S. Chakraverty</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This work investigates the vibration of nonhomogeneous Timoshenko nanobeam resting on the Winkler-Pasternak foundation. Eringen’s nonlocal theory has been used to investigate small-scale effects. The Differential Quadrature method is used to obtain the frequency parameters with various classical boundary conditions. The nonhomogeneous beam model has been considered, where Young’s modulus and density of the beam material vary linearly and quadratically. Convergence of frequency parameters is also discussed. The influence of mechanical properties and scaling parameters on vibration frequencies are investigated for different boundary conditions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Timoshenko%20beam" title="Timoshenko beam">Timoshenko beam</a>, <a href="https://publications.waset.org/abstracts/search?q=Eringen%27s%20nonlocal%20theory" title=" Eringen's nonlocal theory"> Eringen's nonlocal theory</a>, <a href="https://publications.waset.org/abstracts/search?q=differential%20quadrature%20method" title=" differential quadrature method"> differential quadrature method</a>, <a href="https://publications.waset.org/abstracts/search?q=nonhomogeneous%20nanobeam" title=" nonhomogeneous nanobeam"> nonhomogeneous nanobeam</a> </p> <a href="https://publications.waset.org/abstracts/153025/vibration-of-nonhomogeneous-timoshenko-nanobeam-resting-on-winkler-pasternak-foundation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/153025.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">115</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5560</span> Using the Nonlocal Theory of Free Vibrations Nanobeam</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ali%20Oveysi%20Sarabi">Ali Oveysi Sarabi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The dimensions of nanostructures are in the range of inter-atomic spacing of the structures which makes them impossible to be modeled as a continuum. Nanoscale size-effects on vibration analysis of nanobeams embedded in an elastic medium is investigated using different types of beam theory. To this end, Eringen’s nonlocal elasticity is incorporated to various beam theories namely as Euler-Bernoulli beam theory (EBT), Timoshenko beam theory (TBT), Reddy beam theory (RBT), and Levinson beam theory (LBT). The surrounding elastic medium is simulated with both Winkler and Pasternak foundation models and the difference between them is studies. Explicit formulas are presented to obtain the natural frequencies of nanobeam corresponding to each nonlocal beam theory. Selected numerical results are given for different values of the non-local parameter, Winkler modulus parameter, Pasternak modulus parameter and aspect ratio of the beam that imply the effects of them, separately. It is observed that the values of natural frequency are strongly dependent on the stiffness of elastic medium and the value of the non-local parameter and these dependencies varies with the value of aspect ratio and mode number. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=nanobeams" title="nanobeams">nanobeams</a>, <a href="https://publications.waset.org/abstracts/search?q=free%20vibration" title=" free vibration"> free vibration</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlocal%20elasticity" title=" nonlocal elasticity"> nonlocal elasticity</a>, <a href="https://publications.waset.org/abstracts/search?q=winkler%20foundation%20model" title=" winkler foundation model"> winkler foundation model</a>, <a href="https://publications.waset.org/abstracts/search?q=Pasternak%20foundation%20model" title=" Pasternak foundation model"> Pasternak foundation model</a>, <a href="https://publications.waset.org/abstracts/search?q=beam%20theories" title=" beam theories "> beam theories </a> </p> <a href="https://publications.waset.org/abstracts/19886/using-the-nonlocal-theory-of-free-vibrations-nanobeam" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/19886.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">536</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5559</span> Simulation of Propagation of Cos-Gaussian Beam in Strongly Nonlocal Nonlinear Media Using Paraxial Group Transformation </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20Keshavarz">A. Keshavarz</a>, <a href="https://publications.waset.org/abstracts/search?q=Z.%20Roosta"> Z. Roosta</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, propagation of cos-Gaussian beam in strongly nonlocal nonlinear media has been stimulated by using paraxial group transformation. At first, cos-Gaussian beam, nonlocal nonlinear media, critical power, transfer matrix, and paraxial group transformation are introduced. Then, the propagation of the cos-Gaussian beam in strongly nonlocal nonlinear media is simulated. Results show that beam propagation has periodic structure during self-focusing effect in this case. However, this simple method can be used for investigation of propagation of kinds of beams in ABCD optical media. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=paraxial%20group%20transformation" title="paraxial group transformation">paraxial group transformation</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlocal%20nonlinear%20media" title=" nonlocal nonlinear media"> nonlocal nonlinear media</a>, <a href="https://publications.waset.org/abstracts/search?q=cos-Gaussian%20beam" title=" cos-Gaussian beam"> cos-Gaussian beam</a>, <a href="https://publications.waset.org/abstracts/search?q=ABCD%20law" title=" ABCD law"> ABCD law</a> </p> <a href="https://publications.waset.org/abstracts/52660/simulation-of-propagation-of-cos-gaussian-beam-in-strongly-nonlocal-nonlinear-media-using-paraxial-group-transformation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/52660.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">342</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5558</span> Vibration Analysis of Functionally Graded Engesser-Timoshenko Beams Subjected to Axial Load Located on a Continuous Elastic Foundation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20Karami%20Khorramabadi">M. Karami Khorramabadi</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20R.%20Nezamabadi"> A. R. Nezamabadi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper studies free vibration of functionally graded beams Subjected to Axial Load that is simply supported at both ends lies on a continuous elastic foundation. The displacement field of beam is assumed based on Engesser-Timoshenko beam theory. The Young's modulus of beam is assumed to be graded continuously across the beam thickness. Applying the Hamilton's principle, the governing equation is established. Resulting equation is solved using the Euler's Equation. The effects of the constituent volume fractions and foundation coefficient on the vibration frequency are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=functionally%20graded%20beam" title="functionally graded beam">functionally graded beam</a>, <a href="https://publications.waset.org/abstracts/search?q=free%20vibration" title=" free vibration"> free vibration</a>, <a href="https://publications.waset.org/abstracts/search?q=elastic%20foundation" title=" elastic foundation"> elastic foundation</a>, <a href="https://publications.waset.org/abstracts/search?q=Engesser-Timoshenko%20beam%20theory" title=" Engesser-Timoshenko beam theory"> Engesser-Timoshenko beam theory</a> </p> <a href="https://publications.waset.org/abstracts/15081/vibration-analysis-of-functionally-graded-engesser-timoshenko-beams-subjected-to-axial-load-located-on-a-continuous-elastic-foundation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/15081.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">418</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5557</span> A Refined Nonlocal Strain Gradient Theory for Assessing Scaling-Dependent Vibration Behavior of Microbeams</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Xiaobai%20Li">Xiaobai Li</a>, <a href="https://publications.waset.org/abstracts/search?q=Li%20Li"> Li Li</a>, <a href="https://publications.waset.org/abstracts/search?q=Yujin%20Hu"> Yujin Hu</a>, <a href="https://publications.waset.org/abstracts/search?q=Weiming%20Deng"> Weiming Deng</a>, <a href="https://publications.waset.org/abstracts/search?q=Zhe%20Ding"> Zhe Ding</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A size-dependent Euler–Bernoulli beam model, which accounts for nonlocal stress field, strain gradient field and higher order inertia force field, is derived based on the nonlocal strain gradient theory considering velocity gradient effect. The governing equations and boundary conditions are derived both in dimensional and dimensionless form by employed the Hamilton principle. The analytical solutions based on different continuum theories are compared. The effect of higher order inertia terms is extremely significant in high frequency range. It is found that there exists an asymptotic frequency for the proposed beam model, while for the nonlocal strain gradient theory the solutions diverge. The effect of strain gradient field in thickness direction is significant in low frequencies domain and it cannot be neglected when the material strain length scale parameter is considerable with beam thickness. The influence of each of three size effect parameters on the natural frequencies are investigated. The natural frequencies increase with the increasing material strain gradient length scale parameter or decreasing velocity gradient length scale parameter and nonlocal parameter. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Euler-Bernoulli%20Beams" title="Euler-Bernoulli Beams">Euler-Bernoulli Beams</a>, <a href="https://publications.waset.org/abstracts/search?q=free%20vibration" title=" free vibration"> free vibration</a>, <a href="https://publications.waset.org/abstracts/search?q=higher%20order%20inertia" title=" higher order inertia"> higher order inertia</a>, <a href="https://publications.waset.org/abstracts/search?q=Nonlocal%20Strain%20Gradient%20Theory" title=" Nonlocal Strain Gradient Theory"> Nonlocal Strain Gradient Theory</a>, <a href="https://publications.waset.org/abstracts/search?q=velocity%20gradient" title=" velocity gradient"> velocity gradient</a> </p> <a href="https://publications.waset.org/abstracts/60330/a-refined-nonlocal-strain-gradient-theory-for-assessing-scaling-dependent-vibration-behavior-of-microbeams" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/60330.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">267</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5556</span> Nonlinear Analysis of Shear Deformable Deep Beam Resting on Nonlinear Two-Parameter Random Soil</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20Seguini">M. Seguini</a>, <a href="https://publications.waset.org/abstracts/search?q=D.%20Nedjar"> D. Nedjar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, the nonlinear analysis of Timoshenko beam undergoing moderate large deflections and resting on nonlinear two-parameter random foundation is presented, taking into account the effects of shear deformation, beam’s properties variation and the spatial variability of soil characteristics. The finite element probabilistic analysis has been performed by using Timoshenko beam theory with the Von Kàrmàn nonlinear strain-displacement relationships combined to Vanmarcke theory and Monte Carlo simulations, which is implemented in a Matlab program. Numerical examples of the newly developed model is conducted to confirm the efficiency and accuracy of this later and the importance of accounting for the foundation second parameter (Winkler-Pasternak). Thus, the results obtained from the developed model are presented and compared with those available in the literature to examine how the consideration of the shear and spatial variability of soil’s characteristics affects the response of the system. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20analysis" title="nonlinear analysis">nonlinear analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=soil-structure%20interaction" title=" soil-structure interaction"> soil-structure interaction</a>, <a href="https://publications.waset.org/abstracts/search?q=large%20deflection" title=" large deflection"> large deflection</a>, <a href="https://publications.waset.org/abstracts/search?q=Timoshenko%20beam" title=" Timoshenko beam"> Timoshenko beam</a>, <a href="https://publications.waset.org/abstracts/search?q=Euler-Bernoulli%20beam" title=" Euler-Bernoulli beam"> Euler-Bernoulli beam</a>, <a href="https://publications.waset.org/abstracts/search?q=Winkler%20foundation" title=" Winkler foundation"> Winkler foundation</a>, <a href="https://publications.waset.org/abstracts/search?q=Pasternak%20foundation" title=" Pasternak foundation"> Pasternak foundation</a>, <a href="https://publications.waset.org/abstracts/search?q=spatial%20variability" title=" spatial variability"> spatial variability</a> </p> <a href="https://publications.waset.org/abstracts/61881/nonlinear-analysis-of-shear-deformable-deep-beam-resting-on-nonlinear-two-parameter-random-soil" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/61881.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">323</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5555</span> Critical Buckling Load of Carbon Nanotube with Non-Local Timoshenko Beam Using the Differential Transform Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Tayeb%20Bensattalah">Tayeb Bensattalah</a>, <a href="https://publications.waset.org/abstracts/search?q=Mohamed%20Zidour"> Mohamed Zidour</a>, <a href="https://publications.waset.org/abstracts/search?q=Mohamed%20Ait%20Amar%20Meziane"> Mohamed Ait Amar Meziane</a>, <a href="https://publications.waset.org/abstracts/search?q=Tahar%20Hassaine%20Daouadji"> Tahar Hassaine Daouadji</a>, <a href="https://publications.waset.org/abstracts/search?q=Abdelouahed%20Tounsi"> Abdelouahed Tounsi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, the Differential Transform Method (DTM) is employed to predict and to analysis the non-local critical buckling loads of carbon nanotubes with various end conditions and the non-local Timoshenko beam described by single differential equation. The equation differential of buckling of the nanobeams is derived via a non-local theory and the solution for non-local critical buckling loads is finding by the DTM. The DTM is introduced briefly. It can easily be applied to linear or nonlinear problems and it reduces the size of computational work. Inﬂuence of boundary conditions, the chirality of carbon nanotube and aspect ratio on non-local critical buckling loads are studied and discussed. Effects of nonlocal parameter, ratios L/d, the chirality of single-walled carbon nanotube, as well as the boundary conditions on buckling of CNT are investigated. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=boundary%20conditions" title="boundary conditions">boundary conditions</a>, <a href="https://publications.waset.org/abstracts/search?q=buckling" title=" buckling"> buckling</a>, <a href="https://publications.waset.org/abstracts/search?q=non-local" title=" non-local"> non-local</a>, <a href="https://publications.waset.org/abstracts/search?q=differential%20transform%20method" title=" differential transform method"> differential transform method</a> </p> <a href="https://publications.waset.org/abstracts/81382/critical-buckling-load-of-carbon-nanotube-with-non-local-timoshenko-beam-using-the-differential-transform-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/81382.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">301</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5554</span> Molecular Dynamics Simulation of Free Vibration of Graphene Sheets</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Seyyed%20Feisal%20Asbaghian%20Namin">Seyyed Feisal Asbaghian Namin</a>, <a href="https://publications.waset.org/abstracts/search?q=Reza%20Pilafkan"> Reza Pilafkan</a>, <a href="https://publications.waset.org/abstracts/search?q=Mahmood%20Kaffash%20Irzarahimi"> Mahmood Kaffash Irzarahimi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> TThis paper considers vibration of single-layered graphene sheets using molecular dynamics (MD) and nonlocal elasticity theory. Based on the MD simulations, Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS), an open source software, is used to obtain fundamental frequencies. On the other hand, governing equations are derived using nonlocal elasticity and first order shear deformation theory (FSDT) and solved using generalized differential quadrature method (GDQ). The small-scale effect is applied in governing equations of motion by nonlocal parameter. The effect of different side lengths, boundary conditions and nonlocal parameter are inspected for aforementioned methods. Results are obtained from MD simulations is compared with those of the nonlocal elasticity theory to calculate appropriate values for the nonlocal parameter. The nonlocal parameter value is suggested for graphene sheets with various boundary conditions. Furthermore, it is shown that the nonlocal elasticity approach using classical plate theory (CLPT) assumptions overestimates the natural frequencies. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=graphene%20sheets" title="graphene sheets">graphene sheets</a>, <a href="https://publications.waset.org/abstracts/search?q=molecular%20dynamics%20simulations" title=" molecular dynamics simulations"> molecular dynamics simulations</a>, <a href="https://publications.waset.org/abstracts/search?q=fundamental%20frequencies" title=" fundamental frequencies"> fundamental frequencies</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlocal%20elasticity%20theory" title=" nonlocal elasticity theory"> nonlocal elasticity theory</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlocal%20parameter" title=" nonlocal parameter"> nonlocal parameter</a> </p> <a href="https://publications.waset.org/abstracts/57339/molecular-dynamics-simulation-of-free-vibration-of-graphene-sheets" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/57339.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">521</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5553</span> Torsional Vibration of Carbon Nanotubes via Nonlocal Gradient Theories</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mustafa%20Arda">Mustafa Arda</a>, <a href="https://publications.waset.org/abstracts/search?q=Metin%20Aydogdu"> Metin Aydogdu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Carbon nanotubes (CNTs) have many possible application areas because of their superior physical properties. Nonlocal Theory, which unlike the classical theories, includes the size dependency. Nonlocal Stress and Strain Gradient approaches can be used in nanoscale static and dynamic analysis. In the present study, torsional vibration of CNTs was investigated according to nonlocal stress and strain gradient theories. Effects of the small scale parameters to the non-dimensional frequency were obtained. Results were compared with the Molecular Dynamics Simulation and Lattice Dynamics. Strain Gradient Theory has shown more weakening effect on CNT according to the Stress Gradient Theory. Combination of both theories gives more acceptable results rather than the classical and stress or strain gradient theory according to Lattice Dynamics. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=torsional%20vibration" title="torsional vibration">torsional vibration</a>, <a href="https://publications.waset.org/abstracts/search?q=carbon%20nanotubes" title=" carbon nanotubes"> carbon nanotubes</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlocal%20gradient%20theory" title=" nonlocal gradient theory"> nonlocal gradient theory</a>, <a href="https://publications.waset.org/abstracts/search?q=stress" title=" stress"> stress</a>, <a href="https://publications.waset.org/abstracts/search?q=strain" title=" strain"> strain</a> </p> <a href="https://publications.waset.org/abstracts/48828/torsional-vibration-of-carbon-nanotubes-via-nonlocal-gradient-theories" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/48828.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">389</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5552</span> Closed-Form Solutions for Nanobeams Based on the Nonlocal Euler-Bernoulli Theory</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Francesco%20Marotti%20de%20Sciarra">Francesco Marotti de Sciarra</a>, <a href="https://publications.waset.org/abstracts/search?q=Raffaele%20Barretta"> Raffaele Barretta</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Starting from nonlocal continuum mechanics, a thermodynamically new nonlocal model of Euler-Bernoulli nanobeams is provided. The nonlocal variational formulation is consistently provided and the governing differential equation for transverse displacement are presented. Higher-order boundary conditions are then consistently derived. An example is contributed in order to show the effectiveness of the proposed model. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Bernoulli-Euler%20beams" title="Bernoulli-Euler beams">Bernoulli-Euler beams</a>, <a href="https://publications.waset.org/abstracts/search?q=nanobeams" title=" nanobeams"> nanobeams</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlocal%20elasticity" title=" nonlocal elasticity"> nonlocal elasticity</a>, <a href="https://publications.waset.org/abstracts/search?q=closed-form%20solutions" title=" closed-form solutions "> closed-form solutions </a> </p> <a href="https://publications.waset.org/abstracts/24524/closed-form-solutions-for-nanobeams-based-on-the-nonlocal-euler-bernoulli-theory" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/24524.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">369</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5551</span> Forced Vibration of a Planar Curved Beam on Pasternak Foundation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Akif%20Kutlu">Akif Kutlu</a>, <a href="https://publications.waset.org/abstracts/search?q=Merve%20Ermis"> Merve Ermis</a>, <a href="https://publications.waset.org/abstracts/search?q=Nihal%20Eratl%C4%B1"> Nihal Eratlı</a>, <a href="https://publications.waset.org/abstracts/search?q=Mehmet%20H.%20Omurtag"> Mehmet H. Omurtag</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The objective of this study is to investigate the forced vibration analysis of a planar curved beam lying on elastic foundation by using the mixed finite element method. The finite element formulation is based on the Timoshenko beam theory. In order to solve the problems in frequency domain, the element matrices of two nodded curvilinear elements are transformed into Laplace space. The results are transformed back to the time domain by the well-known numerical Modified Durbin’s transformation algorithm. First, the presented finite element formulation is verified through the forced vibration analysis of a planar curved Timoshenko beam resting on Winkler foundation and the finite element results are compared with the results available in the literature. Then, the forced vibration analysis of a planar curved beam resting on Winkler-Pasternak foundation is conducted. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=curved%20beam" title="curved beam">curved beam</a>, <a href="https://publications.waset.org/abstracts/search?q=dynamic%20analysis" title=" dynamic analysis"> dynamic analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=elastic%20foundation" title=" elastic foundation"> elastic foundation</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20element%20method" title=" finite element method"> finite element method</a> </p> <a href="https://publications.waset.org/abstracts/73716/forced-vibration-of-a-planar-curved-beam-on-pasternak-foundation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/73716.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">344</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5550</span> Modal Analysis of Small Frames using High Order Timoshenko Beams</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Chadi%20Azoury">Chadi Azoury</a>, <a href="https://publications.waset.org/abstracts/search?q=Assad%20Kallassy"> Assad Kallassy</a>, <a href="https://publications.waset.org/abstracts/search?q=Pierre%20Rahme"> Pierre Rahme</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we consider the modal analysis of small frames. Firstly, we construct the 3D model using H8 elements and find the natural frequencies of the frame focusing our attention on the modes in the XY plane. Secondly, we construct the 2D model (plane stress model) using Q4 elements. We concluded that the results of both models are very close to each other’s. Then we formulate the stiffness matrix and the mass matrix of the 3-noded Timoshenko beam that is well suited for thick and short beams like in our case. Finally, we model the corners where the horizontal and vertical bar meet with a special matrix. The results of our new model (3-noded Timoshenko beam for the horizontal and vertical bars and a special element for the corners based on the Q4 elements) are very satisfying when performing the modal analysis. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=corner%20element" title="corner element">corner element</a>, <a href="https://publications.waset.org/abstracts/search?q=high-order%20Timoshenko%20beam" title=" high-order Timoshenko beam"> high-order Timoshenko beam</a>, <a href="https://publications.waset.org/abstracts/search?q=Guyan%20reduction" title=" Guyan reduction"> Guyan reduction</a>, <a href="https://publications.waset.org/abstracts/search?q=modal%20analysis%20of%20frames" title=" modal analysis of frames"> modal analysis of frames</a>, <a href="https://publications.waset.org/abstracts/search?q=rigid%20link" title="rigid link">rigid link</a>, <a href="https://publications.waset.org/abstracts/search?q=shear%20locking" title=" shear locking"> shear locking</a>, <a href="https://publications.waset.org/abstracts/search?q=and%20short%20beams" title=" and short beams"> and short beams</a> </p> <a href="https://publications.waset.org/abstracts/24752/modal-analysis-of-small-frames-using-high-order-timoshenko-beams" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/24752.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">318</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5549</span> Thermal Buckling Analysis of Functionally Graded Beams with Various Boundary Conditions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Gholamreza%20Koochaki">Gholamreza Koochaki</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents the buckling analysis of functionally graded beams with various boundary conditions. The first order shear deformation beam theory (Timoshenko beam theory) and the classical theory (Euler-Bernoulli beam theory) of Reddy have been applied to the functionally graded beams buckling analysis The material property gradient is assumed to be in thickness direction. The equilibrium and stability equations are derived using the total potential energy equations, classical theory and first order shear deformation theory assumption. The temperature difference and applied voltage are assumed to be constant. The critical buckling temperature of FG beams are upper than the isotropic ones. Also, the critical temperature is different for various boundary conditions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=buckling" title="buckling">buckling</a>, <a href="https://publications.waset.org/abstracts/search?q=functionally%20graded%20beams" title=" functionally graded beams"> functionally graded beams</a>, <a href="https://publications.waset.org/abstracts/search?q=Hamilton%27s%20principle" title=" Hamilton's principle"> Hamilton's principle</a>, <a href="https://publications.waset.org/abstracts/search?q=Euler-Bernoulli%20beam" title=" Euler-Bernoulli beam"> Euler-Bernoulli beam</a> </p> <a href="https://publications.waset.org/abstracts/30892/thermal-buckling-analysis-of-functionally-graded-beams-with-various-boundary-conditions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/30892.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">392</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5548</span> Evaluation of Dynamic Behavior of a Rotor-Bearing System in Operating Conditions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohammad%20Hadi%20Jalali">Mohammad Hadi Jalali</a>, <a href="https://publications.waset.org/abstracts/search?q=Behrooz%20Shahriari"> Behrooz Shahriari</a>, <a href="https://publications.waset.org/abstracts/search?q=Mostafa%20Ghayour"> Mostafa Ghayour</a>, <a href="https://publications.waset.org/abstracts/search?q=Saeed%20Ziaei-Rad"> Saeed Ziaei-Rad</a>, <a href="https://publications.waset.org/abstracts/search?q=Shahram%20Yousefi"> Shahram Yousefi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Most flexible rotors can be considered as beam-like structures. In many cases, rotors are modeled as one-dimensional bodies, made basically of beam-like shafts with rigid bodies attached to them. This approach is typical of rotor dynamics, both analytical and numerical, and several rotor dynamic codes, based on the finite element method, follow this trend. In this paper, a finite element model based on Timoshenko beam elements is utilized to analyze the lateral dynamic behavior of a certain rotor-bearing system in operating conditions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=finite%20element%20method" title="finite element method">finite element method</a>, <a href="https://publications.waset.org/abstracts/search?q=Timoshenko%20beam%20elements" title=" Timoshenko beam elements"> Timoshenko beam elements</a>, <a href="https://publications.waset.org/abstracts/search?q=operational%20deflection%20shape" title=" operational deflection shape"> operational deflection shape</a>, <a href="https://publications.waset.org/abstracts/search?q=unbalance%20response" title=" unbalance response"> unbalance response</a> </p> <a href="https://publications.waset.org/abstracts/14182/evaluation-of-dynamic-behavior-of-a-rotor-bearing-system-in-operating-conditions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/14182.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">426</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5547</span> Geometrically Linear Symmetric Free Vibration Analysis of Sandwich Beam </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ibnorachid%20Zakaria">Ibnorachid Zakaria</a>, <a href="https://publications.waset.org/abstracts/search?q=El%20Bikri%20Khalid"> El Bikri Khalid</a>, <a href="https://publications.waset.org/abstracts/search?q=Benamar%20Rhali"> Benamar Rhali</a>, <a href="https://publications.waset.org/abstracts/search?q=Farah%20Abdoun"> Farah Abdoun</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The aim of the present work is to study the linear free symmetric vibration of three-layer sandwich beam using the energy method. The zigzag model is used to describe the displacement field. The theoretical model is based on the top and bottom layers behave like Euler-Bernoulli beams while the core layer like a Timoshenko beam. Based on Hamilton’s principle, the governing equation of motion sandwich beam is obtained in order to calculate the linear frequency parameters for a clamped-clamped and simple supported-simple-supported beams. The effects of material properties and geometric parameters on the natural frequencies are also investigated. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=linear%20vibration" title="linear vibration">linear vibration</a>, <a href="https://publications.waset.org/abstracts/search?q=sandwich" title=" sandwich"> sandwich</a>, <a href="https://publications.waset.org/abstracts/search?q=shear%20deformation" title=" shear deformation"> shear deformation</a>, <a href="https://publications.waset.org/abstracts/search?q=Timoshenko%20zig-zag%20model" title=" Timoshenko zig-zag model"> Timoshenko zig-zag model</a> </p> <a href="https://publications.waset.org/abstracts/19506/geometrically-linear-symmetric-free-vibration-analysis-of-sandwich-beam" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/19506.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">472</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5546</span> Dynamic Analysis of Nanosize FG Rectangular Plates Based on Simple Nonlocal Quasi 3D HSDT</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sabrina%20Boutaleb">Sabrina Boutaleb</a>, <a href="https://publications.waset.org/abstracts/search?q=Fouad%20Bourad"> Fouad Bourad</a>, <a href="https://publications.waset.org/abstracts/search?q=Kouider%20Halim%20Benrahou"> Kouider Halim Benrahou</a>, <a href="https://publications.waset.org/abstracts/search?q=Abdelouahed%20Tounsi"> Abdelouahed Tounsi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In the present work, the dynamic analysis of the functionally graded rectangular nanoplates is studied. The theory of nonlocal elasticity based on the quasi 3D high shear deformation theory (quasi 3D HSDT) has been employed to determine the natural frequencies of the nanosized FG plate. In HSDT, a cubic function is employed in terms of thickness coordinates to introduce the influence of transverse shear deformation and stretching thickness. The theory of nonlocal elasticity is utilized to examine the impact of the small scale on the natural frequency of the FG rectangular nanoplate. The equations of motion are deduced by implementing Hamilton’s principle. To demonstrate the accuracy of the proposed method, the calculated results in specific cases are compared and examined with available results in the literature, and a good agreement is observed. Finally, the influence of the various parameters, such as the nonlocal coefficient, the material indexes, the aspect ratio, and the thickness-to-length ratio, on the dynamic properties of the FG nanoplates is illustrated and discussed in detail. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=nonlocal%20elasticity%20theory" title="nonlocal elasticity theory">nonlocal elasticity theory</a>, <a href="https://publications.waset.org/abstracts/search?q=FG%20nanoplate" title=" FG nanoplate"> FG nanoplate</a>, <a href="https://publications.waset.org/abstracts/search?q=free%20vibration" title=" free vibration"> free vibration</a>, <a href="https://publications.waset.org/abstracts/search?q=refined%20theory" title=" refined theory"> refined theory</a>, <a href="https://publications.waset.org/abstracts/search?q=elastic%20foundation" title=" elastic foundation"> elastic foundation</a> </p> <a href="https://publications.waset.org/abstracts/165422/dynamic-analysis-of-nanosize-fg-rectangular-plates-based-on-simple-nonlocal-quasi-3d-hsdt" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/165422.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">120</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5545</span> Biaxial Buckling of Single Layer Graphene Sheet Based on Nonlocal Plate Model and Molecular Dynamics Simulation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=R.%20Pilafkan">R. Pilafkan</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20Kaffash%20Irzarahimi"> M. Kaffash Irzarahimi</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20F.%20Asbaghian%20Namin"> S. F. Asbaghian Namin</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The biaxial buckling behavior of single-layered graphene sheets (SLGSs) is studied in the present work. To consider the size-effects in the analysis, Eringen’s nonlocal elasticity equations are incorporated into classical plate theory (CLPT). A Generalized Differential Quadrature Method (GDQM) approach is utilized and numerical solutions for the critical buckling loads are obtained. Then, molecular dynamics (MD) simulations are performed for a series of zigzag SLGSs with different side-lengths and with various boundary conditions, the results of which are matched with those obtained by the nonlocal plate model to numerical the appropriate values of nonlocal parameter relevant to each type of boundary conditions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=biaxial%20buckling" title="biaxial buckling">biaxial buckling</a>, <a href="https://publications.waset.org/abstracts/search?q=single-layered%20graphene%20sheets" title=" single-layered graphene sheets"> single-layered graphene sheets</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlocal%20elasticity" title=" nonlocal elasticity"> nonlocal elasticity</a>, <a href="https://publications.waset.org/abstracts/search?q=molecular%20dynamics%20simulation" title=" molecular dynamics simulation"> molecular dynamics simulation</a>, <a href="https://publications.waset.org/abstracts/search?q=classical%20plate%20theory" title=" classical plate theory"> classical plate theory</a> </p> <a href="https://publications.waset.org/abstracts/56460/biaxial-buckling-of-single-layer-graphene-sheet-based-on-nonlocal-plate-model-and-molecular-dynamics-simulation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/56460.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">278</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5544</span> Free Vibration Analysis of Symmetric Sandwich Beams</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ibnorachid%20Zakaria">Ibnorachid Zakaria</a>, <a href="https://publications.waset.org/abstracts/search?q=El%20Bikri%20Khalid"> El Bikri Khalid</a>, <a href="https://publications.waset.org/abstracts/search?q=Benamar%20Rhali"> Benamar Rhali</a>, <a href="https://publications.waset.org/abstracts/search?q=Farah%20Abdoun"> Farah Abdoun</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The aim of the present work is to study the linear free symmetric vibration of three-layer sandwich beam using the energy method. The zigzag model is used to describe the displacement field. The theoretical model is based on the top and bottom layers behave like Euler-Bernoulli beams while the core layer like a Timoshenko beam. Based on Hamilton’s principle, the governing equation of motion sandwich beam is obtained in order to calculate the linear frequency parameters for a clamped-clamped and simple supported-simple-supported beams. The effects of material properties and geometric parameters on the natural frequencies are also investigated. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=linear%20vibration" title="linear vibration">linear vibration</a>, <a href="https://publications.waset.org/abstracts/search?q=sandwich" title=" sandwich"> sandwich</a>, <a href="https://publications.waset.org/abstracts/search?q=shear%20deformation" title=" shear deformation"> shear deformation</a>, <a href="https://publications.waset.org/abstracts/search?q=Timoshenko%20zig-zag%20model" title=" Timoshenko zig-zag model"> Timoshenko zig-zag model</a> </p> <a href="https://publications.waset.org/abstracts/20383/free-vibration-analysis-of-symmetric-sandwich-beams" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/20383.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">474</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5543</span> Coupled Flexural-Lateral-Torsional of Shear Deformable Thin-Walled Beams with Asymmetric Cross-Section–Closed Form Exact Solution</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohammed%20Ali%20Hjaji">Mohammed Ali Hjaji</a>, <a href="https://publications.waset.org/abstracts/search?q=Magdi%20Mohareb"> Magdi Mohareb</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper develops the exact solutions for coupled flexural-lateral-torsional static response of thin-walled asymmetric open members subjected to general loading. Using the principle of stationary total potential energy, the governing differential equations of equilibrium are formulated as well as the associated boundary conditions. The formulation is based on a generalized Timoshenko-Vlasov beam theory and accounts for the effects of shear deformation due to bending and warping, and captures the effects of flexural–torsional coupling due to cross-section asymmetry. Closed-form solutions are developed for cantilever and simply supported beams under various forces. In order to demonstrate the validity and the accuracy of this solution, numerical examples are presented and compared with well-established ABAQUS finite element solutions and other numerical results available in the literature. In addition, the results are compared against non-shear deformable beam theories in order to demonstrate the shear deformation effects. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=asymmetric%20cross-section" title="asymmetric cross-section">asymmetric cross-section</a>, <a href="https://publications.waset.org/abstracts/search?q=flexural-lateral-torsional%20response" title=" flexural-lateral-torsional response"> flexural-lateral-torsional response</a>, <a href="https://publications.waset.org/abstracts/search?q=Vlasov-Timoshenko%20beam%20theory" title=" Vlasov-Timoshenko beam theory"> Vlasov-Timoshenko beam theory</a>, <a href="https://publications.waset.org/abstracts/search?q=closed%20form%20solution" title=" closed form solution"> closed form solution</a> </p> <a href="https://publications.waset.org/abstracts/13320/coupled-flexural-lateral-torsional-of-shear-deformable-thin-walled-beams-with-asymmetric-cross-section-closed-form-exact-solution" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/13320.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">469</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5542</span> Vibration of a Beam on an Elastic Foundation Using the Variational Iteration Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Desmond%20Adair">Desmond Adair</a>, <a href="https://publications.waset.org/abstracts/search?q=Kairat%20Ismailov"> Kairat Ismailov</a>, <a href="https://publications.waset.org/abstracts/search?q=Martin%20Jaeger"> Martin Jaeger</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Modelling of Timoshenko beams on elastic foundations has been widely used in the analysis of buildings, geotechnical problems, and, railway and aerospace structures. For the elastic foundation, the most widely used models are one-parameter mechanical models or two-parameter models to include continuity and cohesion of typical foundations, with the two-parameter usually considered the better of the two. Knowledge of free vibration characteristics of beams on an elastic foundation is considered necessary for optimal design solutions in many engineering applications, and in this work, the efficient and accurate variational iteration method is developed and used to calculate natural frequencies of a Timoshenko beam on a two-parameter foundation. The variational iteration method is a technique capable of dealing with some linear and non-linear problems in an easy and efficient way. The calculations are compared with those using a finite-element method and other analytical solutions, and it is shown that the results are accurate and are obtained efficiently. It is found that the effect of the presence of the two-parameter foundation is to increase the beam’s natural frequencies and this is thought to be because of the shear-layer stiffness, which has an effect on the elastic stiffness. By setting the two-parameter model’s stiffness parameter to zero, it is possible to obtain a one-parameter foundation model, and so, comparison between the two foundation models is also made. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Timoshenko%20beam" title="Timoshenko beam">Timoshenko beam</a>, <a href="https://publications.waset.org/abstracts/search?q=variational%20iteration%20method" title=" variational iteration method"> variational iteration method</a>, <a href="https://publications.waset.org/abstracts/search?q=two-parameter%20elastic%20foundation%20model" title=" two-parameter elastic foundation model"> two-parameter elastic foundation model</a> </p> <a href="https://publications.waset.org/abstracts/95779/vibration-of-a-beam-on-an-elastic-foundation-using-the-variational-iteration-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/95779.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">193</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5541</span> Three Dimensional Vibration Analysis of Carbon Nanotubes Embedded in Elastic Medium </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20Shaban">M. Shaban</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20Alibeigloo"> A. Alibeigloo</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper studies free vibration behavior of single-walled carbon nanotubes (SWCNTs) embedded on elastic medium based on three-dimensional theory of elasticity. To accounting the size effect of carbon nanotubes, nonlocal theory is adopted to shell model. The nonlocal parameter is incorporated into all constitutive equations in three dimensions. The surrounding medium is modeled as two-parameter elastic foundation. By using Fourier series expansion in axial and circumferential direction, the set of coupled governing equations are reduced to the ordinary differential equations in thickness direction. Then, the state-space method as an efficient and accurate method is used to solve the resulting equations analytically. Comprehensive parametric studies are carried out to show the influences of the nonlocal parameter, radial and shear elastic stiffness, thickness-to-radius ratio and radius-to-length ratio. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=carbon%20nanotubes" title="carbon nanotubes">carbon nanotubes</a>, <a href="https://publications.waset.org/abstracts/search?q=embedded" title=" embedded"> embedded</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlocal" title=" nonlocal"> nonlocal</a>, <a href="https://publications.waset.org/abstracts/search?q=free%20vibration" title=" free vibration "> free vibration </a> </p> <a href="https://publications.waset.org/abstracts/10246/three-dimensional-vibration-analysis-of-carbon-nanotubes-embedded-in-elastic-medium" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/10246.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">450</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5540</span> Nonlocal Phenomena in Quantum Mechanics</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Kazim%20G.%20Atman">Kazim G. Atman</a>, <a href="https://publications.waset.org/abstracts/search?q=H%C3%BCseyin%20Sirin"> Hüseyin Sirin</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In theoretical physics, nonlocal phenomena has always been subject of debate. However, in the conventional mathematical approach where the developments of the physical systems are investigated by using the standard mathematical tools, nonlocal effects are not taken into account. In order to investigate the nonlocality in quantum mechanics and fractal property of space, fractional derivative operators are employed in this study. In this manner, fractional creation and annihilation operators are introduced and Einstein coefficients are taken into account as an application of concomitant formalism in quantum field theory. Therefore, each energy mode of photons are considered as fractional quantized harmonic oscillator hereby Einstein coefficients are obtained. Nevertheless, wave function and energy eigenvalues of fractional quantum mechanical harmonic oscillator are obtained via the fractional derivative order α which is a measure of the influence of nonlocal effects. In the case α = 1, where space becomes homogeneous and continuous, standard physical conclusions are recovered. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Einstein%E2%80%99s%20Coefficients" title="Einstein’s Coefficients">Einstein’s Coefficients</a>, <a href="https://publications.waset.org/abstracts/search?q=Fractional%20Calculus" title=" Fractional Calculus"> Fractional Calculus</a>, <a href="https://publications.waset.org/abstracts/search?q=Fractional%20Quantum%20Mechanics" title=" Fractional Quantum Mechanics"> Fractional Quantum Mechanics</a>, <a href="https://publications.waset.org/abstracts/search?q=Nonlocal%20Theories" title=" Nonlocal Theories"> Nonlocal Theories</a> </p> <a href="https://publications.waset.org/abstracts/124566/nonlocal-phenomena-in-quantum-mechanics" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/124566.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">169</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5539</span> Molecular Dynamics Simulation for Buckling Analysis at Nanocomposite Beams</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Babak%20Safaei">Babak Safaei</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20M.%20Fattahi"> A. M. Fattahi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In the present study we have investigated axial buckling characteristics of nanocomposite beams reinforced by single-walled carbon nanotubes (SWCNTs). Various types of beam theories including Euler-Bernoulli beam theory, Timoshenko beam theory and Reddy beam theory were used to analyze the buckling behavior of carbon nanotube-reinforced composite beams. Generalized differential quadrature (GDQ) method was utilized to discretize the governing differential equations along with four commonly used boundary conditions. The material properties of the nanocomposite beams were obtained using molecular dynamic (MD) simulation corresponding to both short-(10,10) SWCNT and long-(10,10) SWCNT composites which were embedded by amorphous polyethylene matrix. Then the results obtained directly from MD simulations were matched with those calculated by the mixture rule to extract appropriate values of carbon nanotube efficiency parameters accounting for the scale-dependent material properties. The selected numerical results were presented to indicate the influences of nanotube volume fractions and end supports on the critical axial buckling loads of nanocomposite beams relevant to long- and short-nanotube composites. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=nanocomposites" title="nanocomposites">nanocomposites</a>, <a href="https://publications.waset.org/abstracts/search?q=molecular%20dynamics%20simulation" title=" molecular dynamics simulation"> molecular dynamics simulation</a>, <a href="https://publications.waset.org/abstracts/search?q=axial%20buckling" title=" axial buckling"> axial buckling</a>, <a href="https://publications.waset.org/abstracts/search?q=generalized%20differential%20quadrature%20%28GDQ%29" title=" generalized differential quadrature (GDQ)"> generalized differential quadrature (GDQ)</a> </p> <a href="https://publications.waset.org/abstracts/38174/molecular-dynamics-simulation-for-buckling-analysis-at-nanocomposite-beams" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/38174.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">325</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5538</span> Dynamic Response of Nano Spherical Shell Subjected to Termo-Mechanical Shock Using Nonlocal Elasticity Theory</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=J.%20Ranjbarn">J. Ranjbarn</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20Alibeigloo"> A. Alibeigloo</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we present an analytical method for analysis of nano-scale spherical shell subjected to thermo-mechanical shocks based on nonlocal elasticity theory. Thermo-mechanical properties of nano shpere is assumed to be temperature dependent. Governing partial differential equation of motion is solved analytically by using Laplace transform for time domain and power series for spacial domain. The results in Laplace domain is transferred to time domain by employing the fast inverse Laplace transform (FLIT) method. Accuracy of present approach is assessed by comparing the the numerical results with the results of published work in literature. Furtheremore, the effects of non-local parameter and wall thickness on the dynamic characteristics of the nano-sphere are studied. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=nano-scale%20spherical%20shell" title="nano-scale spherical shell">nano-scale spherical shell</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlocal%20elasticity%20theory" title=" nonlocal elasticity theory"> nonlocal elasticity theory</a>, <a href="https://publications.waset.org/abstracts/search?q=thermomechanical%20shock" title=" thermomechanical shock"> thermomechanical shock</a>, <a href="https://publications.waset.org/abstracts/search?q=dynamic%20response" title=" dynamic response"> dynamic response</a> </p> <a href="https://publications.waset.org/abstracts/10273/dynamic-response-of-nano-spherical-shell-subjected-to-termo-mechanical-shock-using-nonlocal-elasticity-theory" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/10273.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">373</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5537</span> Flutter Control Analysis of an Aircraft Wing Using Carbon Nanotubes Reinforced Polymer</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Timothee%20Gidenne">Timothee Gidenne</a>, <a href="https://publications.waset.org/abstracts/search?q=Xia%20Pinqi"> Xia Pinqi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, an investigation of the use of carbon nanotubes (CNTs) reinforced polymer as an actuator for an active flutter suppression to counter the flutter phenomena is conducted. The goal of this analysis is to establish a link between the behavior of the control surface and the actuators to demonstrate the veracity of using such a suppression system for the aeronautical field. A preliminary binary flutter model using simplified unsteady aerodynamics is developed to study the behavior of the wing while reaching the flutter speed and when the control system suppresses the flutter phenomena. The Timoshenko beam theory for bilayer materials is used to match the response of the control surface with the CNTs reinforced polymer (CNRP) actuators. According to Timoshenko theory, results show a good and realistic response for such a purpose. Even if the results are still preliminary, they show evidence of the potential use of CNRP for control surface actuation for the small-scale and lightweight system. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=actuators" title="actuators">actuators</a>, <a href="https://publications.waset.org/abstracts/search?q=aeroelastic" title=" aeroelastic"> aeroelastic</a>, <a href="https://publications.waset.org/abstracts/search?q=aeroservoelasticity" title=" aeroservoelasticity"> aeroservoelasticity</a>, <a href="https://publications.waset.org/abstracts/search?q=carbon%20nanotubes" title=" carbon nanotubes"> carbon nanotubes</a>, <a href="https://publications.waset.org/abstracts/search?q=flutter" title=" flutter"> flutter</a>, <a href="https://publications.waset.org/abstracts/search?q=flutter%20suppression" title=" flutter suppression"> flutter suppression</a> </p> <a href="https://publications.waset.org/abstracts/114981/flutter-control-analysis-of-an-aircraft-wing-using-carbon-nanotubes-reinforced-polymer" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/114981.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">128</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5536</span> Vibration Analysis of Magnetostrictive Nano-Plate by Using Modified Couple Stress and Nonlocal Elasticity Theories</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hamed%20Khani%20Arani">Hamed Khani Arani</a>, <a href="https://publications.waset.org/abstracts/search?q=Mohammad%20Shariyat"> Mohammad Shariyat</a>, <a href="https://publications.waset.org/abstracts/search?q=Armaghan%20Mohammadian"> Armaghan Mohammadian</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In the present study, the free vibration of magnetostrictive nano-plate (MsNP) resting on the Pasternak foundation is investigated. Firstly, the modified couple stress (MCS) and nonlocal elasticity theories are compared together and taken into account to consider the small scale effects; in this paper not only two theories are analyzed but also it improves the MCS theory is more accurate than nonlocal elasticity theory in such problems. A feedback control system is utilized to investigate the effects of a magnetic field. First-order shear deformation theory (FSDT), Hamilton’s principle and energy method are utilized in order to drive the equations of motion and these equations are solved by differential quadrature method (DQM) for simply supported boundary conditions. The MsNP undergoes in-plane forces in <em>x </em>and <em>y </em>directions. In this regard, the dimensionless frequency is plotted to study the effects of small scale parameter, magnetic field, aspect ratio, thickness ratio and compression and tension loads. Results indicate that these parameters play a key role on the natural frequency. According to the above results, MsNP can be used in the communications equipment, smart control vibration of nanostructure especially in sensor and actuators such as wireless linear micro motor and smart nano valves in injectors. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=feedback%20control%20system" title="feedback control system">feedback control system</a>, <a href="https://publications.waset.org/abstracts/search?q=magnetostrictive%20nano-plate" title=" magnetostrictive nano-plate"> magnetostrictive nano-plate</a>, <a href="https://publications.waset.org/abstracts/search?q=modified%20couple%20stress%20theory" title=" modified couple stress theory"> modified couple stress theory</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlocal%20elasticity%20theory" title=" nonlocal elasticity theory"> nonlocal elasticity theory</a>, <a href="https://publications.waset.org/abstracts/search?q=vibration%20analysis" title=" vibration analysis"> vibration analysis</a> </p> <a href="https://publications.waset.org/abstracts/126379/vibration-analysis-of-magnetostrictive-nano-plate-by-using-modified-couple-stress-and-nonlocal-elasticity-theories" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/126379.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">135</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5535</span> Analysis of Thermal Effect on Functionally Graded Micro-Beam via Mixed Finite Element Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Cagri%20Mollamahmutoglu">Cagri Mollamahmutoglu</a>, <a href="https://publications.waset.org/abstracts/search?q=Ali%20Mercan"> Ali Mercan</a>, <a href="https://publications.waset.org/abstracts/search?q=Aykut%20Levent"> Aykut Levent</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Studies concerning the microstructures are becoming more important as the utilization of various micro-electro mechanical systems (MEMS) are increasing. Thus in recent years, thermal buckling and vibration analysis of microstructures have been subject to many investigations that are utilizing different numerical methods. In this study, thermal effects on mechanical response of a functionally graded (FG) Timoshenko micro-beam are presented in the framework of a mixed finite element formulation. Size effects are taken into consideration via modified couple stress theory. The mixed formulation is based on a function which in turn is derived via Gateaux Differential scientifically. After the resolution of all field equations of the beam, a potential operator is carefully constructed. Then this operator is used for the manufacturing of the functional. Usual procedures of finite element approximation are utilized for the derivation of the mixed finite element equations once the potential is obtained. Resulting finite element formulation allows usage of C₀ type simple linear shape functions and avoids shear-locking phenomena, which is a common shortcoming of the displacement-based formulations of moderately thick beams. The developed numerical scheme is used to obtain the effects of thermal loads on the static bending, free vibration and buckling of FG Timoshenko micro-beams for different power-law parameters, aspect ratios and boundary conditions. The versatility of the mixed formulation is presented over other numerical methods such as generalized differential quadrature method (GDQM). Another attractive property of the formulation is that it allows direct calculation of the contribution of micro effects on the overall mechanical response. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=micro-beam" title="micro-beam">micro-beam</a>, <a href="https://publications.waset.org/abstracts/search?q=functionally%20graded%20materials" title=" functionally graded materials"> functionally graded materials</a>, <a href="https://publications.waset.org/abstracts/search?q=thermal%20effect" title=" thermal effect"> thermal effect</a>, <a href="https://publications.waset.org/abstracts/search?q=mixed%20finite%20element%20method" title=" mixed finite element method"> mixed finite element method</a> </p> <a href="https://publications.waset.org/abstracts/113349/analysis-of-thermal-effect-on-functionally-graded-micro-beam-via-mixed-finite-element-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/113349.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">138</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5534</span> A Study on Application of Elastic Theory for Computing Flexural Stresses in Preflex Beam</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Nasiri%20Ahmadullah">Nasiri Ahmadullah</a>, <a href="https://publications.waset.org/abstracts/search?q=Shimozato%20Tetsuhiro"> Shimozato Tetsuhiro</a>, <a href="https://publications.waset.org/abstracts/search?q=Masayuki%20Tai"> Masayuki Tai</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents the step-by-step procedure for using Elastic Theory to calculate the internal stresses in composite bridge girders prestressed by the Preflexing Technology, called Prebeam in Japan and Preflex beam worldwide. Elastic Theory approaches preflex beams the same way as it does the conventional composite girders. Since preflex beam undergoes different stages of construction, calculations are made using different sectional and material properties. Stresses are calculated in every stage using the properties of the specific section. Stress accumulation gives the available stress in a section of interest. Concrete presence in the section implies prestress loss due to creep and shrinkage, however; more work is required to be done in this field. In addition to the graphical presentation of this application, this paper further discusses important notes of graphical comparison between the results of an experimental-only research carried out on a preflex beam, with the results of simulation based on the elastic theory approach, for an identical beam using Finite Element Modeling (FEM) by the author. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=composite%20girder" title="composite girder">composite girder</a>, <a href="https://publications.waset.org/abstracts/search?q=Elastic%20Theory" title=" Elastic Theory"> Elastic Theory</a>, <a href="https://publications.waset.org/abstracts/search?q=preflex%20beam" title=" preflex beam"> preflex beam</a>, <a href="https://publications.waset.org/abstracts/search?q=prestressing" title=" prestressing"> prestressing</a> </p> <a href="https://publications.waset.org/abstracts/64680/a-study-on-application-of-elastic-theory-for-computing-flexural-stresses-in-preflex-beam" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/64680.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">279</span> </span> </div> </div> <ul class="pagination"> <li class="page-item disabled"><span class="page-link">&lsaquo;</span></li> <li class="page-item active"><span class="page-link">1</span></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=Nonlocal%20Timoshenko%20beam%20theory&page=2">2</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=Nonlocal%20Timoshenko%20beam%20theory&page=3">3</a></li> <li class="page-item"><a class="page-link" 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