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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> 132</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: Euler</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">132</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">375</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">131</span> Stabilization of the Bernoulli-Euler Plate Equation: Numerical Analysis</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Carla%20E.%20O.%20de%20Moraes">Carla E. O. de Moraes</a>, <a href="https://publications.waset.org/abstracts/search?q=Gladson%20O.%20Antunes"> Gladson O. Antunes</a>, <a href="https://publications.waset.org/abstracts/search?q=Mauro%20A.%20Rincon"> Mauro A. Rincon</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The aim of this paper is to study the internal stabilization of the Bernoulli-Euler equation numerically. For this, we consider a square plate subjected to a feedback/damping force distributed only in a subdomain. An algorithm for obtaining an approximate solution to this problem was proposed and implemented. The numerical method used was the Finite Difference Method. Numerical simulations were performed and showed the behavior of the solution, confirming the theoretical results that have already been proved in the literature. In addition, we studied the validation of the numerical scheme proposed, followed by an analysis of the numerical error; and we conducted a study on the decay of the energy associated. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Bernoulli-Euler%20plate%20equation" title="Bernoulli-Euler plate equation">Bernoulli-Euler plate equation</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20simulations" title=" numerical simulations"> numerical simulations</a>, <a href="https://publications.waset.org/abstracts/search?q=stability" title=" stability"> stability</a>, <a href="https://publications.waset.org/abstracts/search?q=energy%20decay" title=" energy decay"> energy decay</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20difference%20method" title=" finite difference method"> finite difference method</a> </p> <a href="https://publications.waset.org/abstracts/7035/stabilization-of-the-bernoulli-euler-plate-equation-numerical-analysis" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/7035.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">421</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">130</span> A Runge Kutta Discontinuous Galerkin Method for Lagrangian Compressible Euler Equations in Two-Dimensions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Xijun%20Yu">Xijun Yu</a>, <a href="https://publications.waset.org/abstracts/search?q=Zhenzhen%20Li"> Zhenzhen Li</a>, <a href="https://publications.waset.org/abstracts/search?q=Zupeng%20Jia"> Zupeng Jia</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents a new cell-centered Lagrangian scheme for two-dimensional compressible flow. The new scheme uses a semi-Lagrangian form of the Euler equations. The system of equations is discretized by Discontinuous Galerkin (DG) method using the Taylor basis in Eulerian space. The vertex velocities and the numerical fluxes through the cell interfaces are computed consistently by a nodal solver. The mesh moves with the fluid flow. The time marching is implemented by a class of the Runge-Kutta (RK) methods. A WENO reconstruction is used as a limiter for the RKDG method. The scheme is conservative for the mass, momentum and total energy. The scheme maintains second-order accuracy and has free parameters. Results of some numerical tests are presented to demonstrate the accuracy and the robustness of the scheme. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=cell-centered%20Lagrangian%20scheme" title="cell-centered Lagrangian scheme">cell-centered Lagrangian scheme</a>, <a href="https://publications.waset.org/abstracts/search?q=compressible%20Euler%20equations" title=" compressible Euler equations"> compressible Euler equations</a>, <a href="https://publications.waset.org/abstracts/search?q=RKDG%20method" title=" RKDG method"> RKDG method</a> </p> <a href="https://publications.waset.org/abstracts/3584/a-runge-kutta-discontinuous-galerkin-method-for-lagrangian-compressible-euler-equations-in-two-dimensions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/3584.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">554</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">129</span> Fractional Euler Method and Finite Difference Formula Using Conformable Fractional Derivative</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ramzi%20B.%20Albadarneh">Ramzi B. Albadarneh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we use the new definition of fractional derivative called conformable fractional derivative to derive some finite difference formulas and its error terms which are used to solve fractional differential equations and fractional partial differential equations, also to derive fractional Euler method and its error terms which can be applied to solve fractional differential equations. To provide the contribution of our work some applications on finite difference formulas and Euler Method are given. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=conformable%20fractional%20derivative" title="conformable fractional derivative">conformable fractional derivative</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20difference%20formula" title=" finite difference formula"> finite difference formula</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20derivative" title=" fractional derivative"> fractional derivative</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20difference%20formula" title=" finite difference formula"> finite difference formula</a> </p> <a href="https://publications.waset.org/abstracts/37072/fractional-euler-method-and-finite-difference-formula-using-conformable-fractional-derivative" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/37072.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">444</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">128</span> Experimental Investigation of Natural Frequency and Forced Vibration of Euler-Bernoulli Beam under Displacement of Concentrated Mass and Load</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Aref%20Aasi">Aref Aasi</a>, <a href="https://publications.waset.org/abstracts/search?q=Sadegh%20Mehdi%20Aghaei"> Sadegh Mehdi Aghaei</a>, <a href="https://publications.waset.org/abstracts/search?q=Balaji%20Panchapakesan"> Balaji Panchapakesan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This work aims to evaluate the free and forced vibration of a beam with two end joints subjected to a concentrated moving mass and a load using the Euler-Bernoulli method. The natural frequency is calculated for different locations of the concentrated mass and load on the beam. The analytical results are verified by the experimental data. The variations of natural frequency as a function of the location of the mass, the effect of the forced frequency on the vibrational amplitude, and the displacement amplitude versus time are investigated. It is discovered that as the concentrated mass moves toward the center of the beam, the natural frequency of the beam and the relative error between experimental and analytical data decreases. There is a close resemblance between analytical data and experimental observations. <p class="card-text"><strong>Keywords:</strong> <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=natural%20frequency" title=" natural frequency"> natural frequency</a>, <a href="https://publications.waset.org/abstracts/search?q=forced%20vibration" title=" forced vibration"> forced vibration</a>, <a href="https://publications.waset.org/abstracts/search?q=experimental%20setup" title=" experimental setup"> experimental setup</a> </p> <a href="https://publications.waset.org/abstracts/144338/experimental-investigation-of-natural-frequency-and-forced-vibration-of-euler-bernoulli-beam-under-displacement-of-concentrated-mass-and-load" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/144338.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">127</span> Application of the MOOD Technique to the Steady-State Euler Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Gaspar%20J.%20Machado">Gaspar J. Machado</a>, <a href="https://publications.waset.org/abstracts/search?q=St%C3%A9phane%20Clain"> Stéphane Clain</a>, <a href="https://publications.waset.org/abstracts/search?q=Raphael%20Loub%C3%A8re"> Raphael Loubère</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The goal of the present work is to numerically study steady-state nonlinear hyperbolic equations in the context of the finite volume framework. We will consider the unidimensional Burgers' equation as the reference case for the scalar situation and the unidimensional Euler equations for the vectorial situation. We consider two approaches to solve the nonlinear equations: a time marching algorithm and a direct steady-state approach. We first develop the necessary and sufficient conditions to obtain the existence and unicity of the solution. We treat regular examples and solutions with a steady shock and to provide very-high-order finite volume approximations we implement a method based on the MOOD technology (Multi-dimensional Optimal Order Detection). The main ingredient consists in using an 'a posteriori' limiting strategy to eliminate non physical oscillations deriving from the Gibbs phenomenon while keeping a high accuracy for the smooth part. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Euler%20equations" title="Euler equations">Euler equations</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20volume" title=" finite volume"> finite volume</a>, <a href="https://publications.waset.org/abstracts/search?q=MOOD" title=" MOOD"> MOOD</a>, <a href="https://publications.waset.org/abstracts/search?q=steady-state" title=" steady-state"> steady-state</a> </p> <a href="https://publications.waset.org/abstracts/52830/application-of-the-mood-technique-to-the-steady-state-euler-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/52830.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">280</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">126</span> Aeromagnetic Data Interpretation and Source Body Evaluation Using Standard Euler Deconvolution Technique in Obudu Area, Southeastern Nigeria</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Chidiebere%20C.%20Agoha">Chidiebere C. Agoha</a>, <a href="https://publications.waset.org/abstracts/search?q=Chukwuebuka%20N.%20Onwubuariri"> Chukwuebuka N. Onwubuariri</a>, <a href="https://publications.waset.org/abstracts/search?q=Collins%20U.amasike"> Collins U.amasike</a>, <a href="https://publications.waset.org/abstracts/search?q=Tochukwu%20I.%20Mgbeojedo"> Tochukwu I. Mgbeojedo</a>, <a href="https://publications.waset.org/abstracts/search?q=Joy%20O.%20Njoku"> Joy O. Njoku</a>, <a href="https://publications.waset.org/abstracts/search?q=Lawson%20J.%20Osaki"> Lawson J. Osaki</a>, <a href="https://publications.waset.org/abstracts/search?q=Ifeyinwa%20J.%20Ofoh"> Ifeyinwa J. Ofoh</a>, <a href="https://publications.waset.org/abstracts/search?q=Francis%20B.%20Akiang"> Francis B. Akiang</a>, <a href="https://publications.waset.org/abstracts/search?q=Dominic%20N.%20Anuforo"> Dominic N. Anuforo</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In order to interpret the airborne magnetic data and evaluate the approximate location, depth, and geometry of the magnetic sources within Obudu area using the standard Euler deconvolution method, very high-resolution aeromagnetic data over the area was acquired, processed digitally and analyzed using Oasis Montaj 8.5 software. Data analysis and enhancement techniques, including reduction to the equator, horizontal derivative, first and second vertical derivatives, upward continuation and regional-residual separation, were carried out for the purpose of detailed data Interpretation. Standard Euler deconvolution for structural indices of 0, 1, 2, and 3 was also carried out and respective maps were obtained using the Euler deconvolution algorithm. Results show that the total magnetic intensity ranges from -122.9nT to 147.0nT, regional intensity varies between -106.9nT to 137.0nT, while residual intensity ranges between -51.5nT to 44.9nT clearly indicating the masking effect of deep-seated structures over surface and shallow subsurface magnetic materials. Results also indicated that the positive residual anomalies have an NE-SW orientation, which coincides with the trend of major geologic structures in the area. Euler deconvolution for all the considered structural indices has depth to magnetic sources ranging from the surface to more than 2000m. Interpretation of the various structural indices revealed the locations and depths of the source bodies and the existence of geologic models, including sills, dykes, pipes, and spherical structures. This area is characterized by intrusive and very shallow basement materials and represents an excellent prospect for solid mineral exploration and development. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Euler%20deconvolution" title="Euler deconvolution">Euler deconvolution</a>, <a href="https://publications.waset.org/abstracts/search?q=horizontal%20derivative" title=" horizontal derivative"> horizontal derivative</a>, <a href="https://publications.waset.org/abstracts/search?q=Obudu" title=" Obudu"> Obudu</a>, <a href="https://publications.waset.org/abstracts/search?q=structural%20indices" title=" structural indices"> structural indices</a> </p> <a href="https://publications.waset.org/abstracts/171696/aeromagnetic-data-interpretation-and-source-body-evaluation-using-standard-euler-deconvolution-technique-in-obudu-area-southeastern-nigeria" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/171696.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">89</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">125</span> A Posteriori Analysis of the Spectral Element Discretization of Heat Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Chor%20Nejmeddine">Chor Nejmeddine</a>, <a href="https://publications.waset.org/abstracts/search?q=Ines%20Ben%20Omrane"> Ines Ben Omrane</a>, <a href="https://publications.waset.org/abstracts/search?q=Mohamed%20Abdelwahed"> Mohamed Abdelwahed</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we present a posteriori analysis of the discretization of the heat equation by spectral element method. We apply Euler's implicit scheme in time and spectral method in space. We propose two families of error indicators, both of which are built from the residual of the equation and we prove that they satisfy some optimal estimates. We present some numerical results which are coherent with the theoretical ones. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=heat%20equation" title="heat equation">heat equation</a>, <a href="https://publications.waset.org/abstracts/search?q=spectral%20elements%20discretization" title=" spectral elements discretization"> spectral elements discretization</a>, <a href="https://publications.waset.org/abstracts/search?q=error%20indicators" title=" error indicators"> error indicators</a>, <a href="https://publications.waset.org/abstracts/search?q=Euler" title=" Euler"> Euler</a> </p> <a href="https://publications.waset.org/abstracts/4041/a-posteriori-analysis-of-the-spectral-element-discretization-of-heat-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/4041.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">315</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">124</span> Comparing Numerical Accuracy of Solutions of Ordinary Differential Equations (ODE) Using Taylor's Series Method, Euler's Method and Runge-Kutta (RK) Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Palwinder%20Singh">Palwinder Singh</a>, <a href="https://publications.waset.org/abstracts/search?q=Munish%20Sandhir"> Munish Sandhir</a>, <a href="https://publications.waset.org/abstracts/search?q=Tejinder%20Singh"> Tejinder Singh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The ordinary differential equations (ODE) represent a natural framework for mathematical modeling of many real-life situations in the field of engineering, control systems, physics, chemistry and astronomy etc. Such type of differential equations can be solved by analytical methods or by numerical methods. If the solution is calculated using analytical methods, it is done through calculus theories, and thus requires a longer time to solve. In this paper, we compare the numerical accuracy of the solutions given by the three main types of one-step initial value solvers: Taylor’s Series Method, Euler’s Method and Runge-Kutta Fourth Order Method (RK4). The comparison of accuracy is obtained through comparing the solutions of ordinary differential equation given by these three methods. Furthermore, to verify the accuracy; we compare these numerical solutions with the exact solutions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ordinary%20differential%20equations%20%28ODE%29" title="Ordinary differential equations (ODE)">Ordinary differential equations (ODE)</a>, <a href="https://publications.waset.org/abstracts/search?q=Taylor%E2%80%99s%20Series%20Method" title=" Taylor’s Series Method"> Taylor’s Series Method</a>, <a href="https://publications.waset.org/abstracts/search?q=Euler%E2%80%99s%20Method" title=" Euler’s Method"> Euler’s Method</a>, <a href="https://publications.waset.org/abstracts/search?q=Runge-Kutta%20Fourth%20Order%20Method" title=" Runge-Kutta Fourth Order Method"> Runge-Kutta Fourth Order Method</a> </p> <a href="https://publications.waset.org/abstracts/56685/comparing-numerical-accuracy-of-solutions-of-ordinary-differential-equations-ode-using-taylors-series-method-eulers-method-and-runge-kutta-rk-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/56685.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">364</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">123</span> Load Maximization of Two-Link Flexible Manipulator Using Suppression Vibration with Piezoelectric Transducer</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hamidreza%20Heidari">Hamidreza Heidari</a>, <a href="https://publications.waset.org/abstracts/search?q=Abdollah%20Malmir%20Nasab"> Abdollah Malmir Nasab</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, the energy equations of a two-link flexible manipulator were extracted using the Euler-Bernoulli beam hypotheses. Applying Assumed mode and considering some finite degrees of freedom, we could obtain dynamic motions of each manipulator using Euler-Lagrange equations. Using its claws, the robots can carry a certain load with the ached control of vibrations for robot flexible links during the travelling path using the piezoceramics transducer; dynamic load carrying capacity increase. The traveling path of flexible robot claw has been taken from that of equivalent rigid manipulator and coupled; therefore to avoid the role of Euler-Bernoulli beam assumptions and linear strains, material and physical characteristics selection of robot cause deflection of link ends not exceed 5% of link length. To do so, the maximum load carrying capacity of robot is calculated at the horizontal plan. The increasing of robot load carrying capacity with vibration control is 53%. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=flexible%20link" title="flexible link">flexible link</a>, <a href="https://publications.waset.org/abstracts/search?q=DLCC" title=" DLCC"> DLCC</a>, <a href="https://publications.waset.org/abstracts/search?q=active%20control%20vibration" title=" active control vibration"> active control vibration</a>, <a href="https://publications.waset.org/abstracts/search?q=assumed%20mode%20method" title=" assumed mode method"> assumed mode method</a> </p> <a href="https://publications.waset.org/abstracts/54871/load-maximization-of-two-link-flexible-manipulator-using-suppression-vibration-with-piezoelectric-transducer" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/54871.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">404</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">122</span> Euler-Bernoulli’s Approach for Buckling Analysis of Thick Rectangular Plates Using Alternative I Refined Theory</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Owus%20Mathias%20Ibearugbulem">Owus Mathias Ibearugbulem</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The study presents Euler-Bernoulli’s approach for buckling analysis of thick rectangular plates using alternative I refined theory. No earlier study, to the best knowledge of the author, based on the literature available to this research, applied Euler-Bernoulli’s approach in the alternative I refined theory for buckling analysis of thick rectangular plates. In this study, basic kinematics and constitutive relations for thick rectangular plates are employed in the differential equations of equilibrium of stresses in a deformable elemental body to obtain alternative I governing differential equations of thick rectangular plates and the corresponding compatibility equations. Solving these equations resulted in a general deflection function of a thick rectangular plate. Using this function and satisfying the boundary conditions of three plates, their peculiar deflection functions are obtained. Going further, the study determined the non-dimensional critical buckling loads of the six plates. Values of the non-dimensional critical buckling load from the present study are compared with those from a three-dimensional buckling analysis of a thick plate. The highest percentage difference recorded for the plates: all edges simply supported (ssss), all edges clamped (cccc) and adjacent edges clamped with the other edges simply supported (ccss) are 3.31%, 5.57% and 3.38% respectively. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Euler-Bernoulli" title="Euler-Bernoulli">Euler-Bernoulli</a>, <a href="https://publications.waset.org/abstracts/search?q=buckling" title=" buckling"> buckling</a>, <a href="https://publications.waset.org/abstracts/search?q=alternative%20I" title=" alternative I"> alternative I</a>, <a href="https://publications.waset.org/abstracts/search?q=kinematics" title=" kinematics"> kinematics</a>, <a href="https://publications.waset.org/abstracts/search?q=constitutive%20relation" title=" constitutive relation"> constitutive relation</a>, <a href="https://publications.waset.org/abstracts/search?q=governing%20differential%20equation" title=" governing differential equation"> governing differential equation</a>, <a href="https://publications.waset.org/abstracts/search?q=compatibility%20equation" title=" compatibility equation"> compatibility equation</a>, <a href="https://publications.waset.org/abstracts/search?q=thick%20plate" title=" thick plate"> thick plate</a> </p> <a href="https://publications.waset.org/abstracts/188996/euler-bernoullis-approach-for-buckling-analysis-of-thick-rectangular-plates-using-alternative-i-refined-theory" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/188996.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">38</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">121</span> An Approximation Method for Exact Boundary Controllability of Euler-Bernoulli</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20Khernane">A. Khernane</a>, <a href="https://publications.waset.org/abstracts/search?q=N.%20Khelil"> N. Khelil</a>, <a href="https://publications.waset.org/abstracts/search?q=L.%20Djerou"> L. Djerou</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The aim of this work is to study the numerical implementation of the Hilbert uniqueness method for the exact boundary controllability of Euler-Bernoulli beam equation. This study may be difficult. This will depend on the problem under consideration (geometry, control, and dimension) and the numerical method used. Knowledge of the asymptotic behaviour of the control governing the system at time T may be useful for its calculation. This idea will be developed in this study. We have characterized as a first step the solution by a minimization principle and proposed secondly a method for its resolution to approximate the control steering the considered system to rest at time T. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=boundary%20control" title="boundary control">boundary control</a>, <a href="https://publications.waset.org/abstracts/search?q=exact%20controllability" title=" exact controllability"> exact controllability</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20difference%20methods" title=" finite difference methods"> finite difference methods</a>, <a href="https://publications.waset.org/abstracts/search?q=functional%20optimization" title=" functional optimization"> functional optimization</a> </p> <a href="https://publications.waset.org/abstracts/37074/an-approximation-method-for-exact-boundary-controllability-of-euler-bernoulli" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/37074.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">352</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">120</span> A Quadcopter Stability Analysis: A Case Study Using Simulation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=C.%20S.%20Bianca%20Sabrina">C. S. Bianca Sabrina</a>, <a href="https://publications.waset.org/abstracts/search?q=N.%20Egidio%20Raimundo"> N. Egidio Raimundo</a>, <a href="https://publications.waset.org/abstracts/search?q=L.%20Alexandre%20Baratella"> L. Alexandre Baratella</a>, <a href="https://publications.waset.org/abstracts/search?q=C.%20H.%20Jo%C3%A3o%20Paulo"> C. H. João Paulo</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper aims to present a study, with the theoretical concepts and applications of the Quadcopter, using the MATLAB simulator. In order to use this tool, the study of the stability of the drone through a Proportional - Integral - Derivative (PID) controller will be presented. After the stability study, some tests are done on the simulator and its results will be presented. From the mathematical model, it is possible to find the Newton-Euler angles, so that it is possible to stabilize the quadcopter in a certain position in the air, starting from the ground. In order to understand the impact of the controllers gain values on the stabilization of the Euler-Newton angles, three conditions will be tested with different controller gain values. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=controllers" title="controllers">controllers</a>, <a href="https://publications.waset.org/abstracts/search?q=drones" title=" drones"> drones</a>, <a href="https://publications.waset.org/abstracts/search?q=quadcopter" title=" quadcopter"> quadcopter</a>, <a href="https://publications.waset.org/abstracts/search?q=stability" title=" stability"> stability</a> </p> <a href="https://publications.waset.org/abstracts/129262/a-quadcopter-stability-analysis-a-case-study-using-simulation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/129262.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">204</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">119</span> 3D Codes for Unsteady Interaction Problems of Continuous Mechanics in Euler Variables</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20Abuziarov">M. Abuziarov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The designed complex is intended for the numerical simulation of fast dynamic processes of interaction of heterogeneous environments susceptible to the significant formability. The main challenges in solving such problems are associated with the construction of the numerical meshes. Currently, there are two basic approaches to solve this problem. One is using of Lagrangian or Lagrangian Eulerian grid associated with the boundaries of media and the second is associated with the fixed Eulerian mesh, boundary cells of which cut boundaries of the environment medium and requires the calculation of these cut volumes. Both approaches require the complex grid generators and significant time for preparing the code’s data for simulation. In this codes these problems are solved using two grids, regular fixed and mobile local Euler Lagrange - Eulerian (ALE approach) accompanying the contact and free boundaries, the surfaces of shock waves and phase transitions, and other possible features of solutions, with mutual interpolation of integrated parameters. For modeling of both liquids and gases, and deformable solids the Godunov scheme of increased accuracy is used in Lagrangian - Eulerian variables, the same for the Euler equations and for the Euler- Cauchy, describing the deformation of the solid. The increased accuracy of the scheme is achieved by using 3D spatial time dependent solution of the discontinuity problem (3D space time dependent Riemann's Problem solver). The same solution is used to calculate the interaction at the liquid-solid surface (Fluid Structure Interaction problem). The codes does not require complex 3D mesh generators, only the surfaces of the calculating objects as the STL files created by means of engineering graphics are given by the user, which greatly simplifies the preparing the task and makes it convenient to use directly by the designer at the design stage. The results of the test solutions and applications related to the generation and extension of the detonation and shock waves, loading the constructions are presented. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fluid%20structure%20interaction" title="fluid structure interaction">fluid structure interaction</a>, <a href="https://publications.waset.org/abstracts/search?q=Riemann%27s%20solver" title=" Riemann's solver"> Riemann's solver</a>, <a href="https://publications.waset.org/abstracts/search?q=Euler%20variables" title=" Euler variables"> Euler variables</a>, <a href="https://publications.waset.org/abstracts/search?q=3D%20codes" title=" 3D codes"> 3D codes</a> </p> <a href="https://publications.waset.org/abstracts/17837/3d-codes-for-unsteady-interaction-problems-of-continuous-mechanics-in-euler-variables" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/17837.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">442</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">118</span> Hydrodynamic Simulation of Co-Current and Counter Current of Column Distillation Using Euler Lagrange Approach</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=H.%20Troudi">H. Troudi</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20Ghiss"> M. Ghiss</a>, <a href="https://publications.waset.org/abstracts/search?q=Z.%20Tourki"> Z. Tourki</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20Ellejmi"> M. Ellejmi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Packed columns of liquefied petroleum gas (LPG) consists of separating the liquid mixture of propane and butane to pure gas components by the distillation phenomenon. The flow of the gas and liquid inside the columns is operated by two ways: The co-current and the counter current operation. Heat, mass and species transfer between phases represent the most important factors that influence the choice between those two operations. In this paper, both processes are discussed using computational CFD simulation through ANSYS-Fluent software. Only 3D half section of the packed column was considered with one packed bed. The packed bed was characterized in our case as a porous media. The simulations were carried out at transient state conditions. A multi-component gas and liquid mixture were used out in the two processes. We utilized the Euler-Lagrange approach in which the gas was treated as a continuum phase and the liquid as a group of dispersed particles. The heat and the mass transfer process was modeled using multi-component droplet evaporation approach. The results show that the counter-current process performs better than the co-current, although such limitations of our approach are noted. This comparison gives accurate results for computations times higher than 2 s, at different gas velocity and at packed bed porosity of 0.9. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=co-current" title="co-current">co-current</a>, <a href="https://publications.waset.org/abstracts/search?q=counter-current" title=" counter-current"> counter-current</a>, <a href="https://publications.waset.org/abstracts/search?q=Euler-Lagrange%20model" title=" Euler-Lagrange model"> Euler-Lagrange model</a>, <a href="https://publications.waset.org/abstracts/search?q=heat%20transfer" title=" heat transfer"> heat transfer</a>, <a href="https://publications.waset.org/abstracts/search?q=mass%20transfer" title=" mass transfer"> mass transfer</a> </p> <a href="https://publications.waset.org/abstracts/60813/hydrodynamic-simulation-of-co-current-and-counter-current-of-column-distillation-using-euler-lagrange-approach" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/60813.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">217</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">117</span> An Alternative Framework of Multi-Resolution Nested Weighted Essentially Non-Oscillatory Schemes for Solving Euler Equations with Adaptive Order</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Zhenming%20Wang">Zhenming Wang</a>, <a href="https://publications.waset.org/abstracts/search?q=Jun%20Zhu"> Jun Zhu</a>, <a href="https://publications.waset.org/abstracts/search?q=Yuchen%20Yang"> Yuchen Yang</a>, <a href="https://publications.waset.org/abstracts/search?q=Ning%20Zhao"> Ning Zhao</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In the present paper, an alternative framework is proposed to construct a class of finite difference multi-resolution nested weighted essentially non-oscillatory (WENO) schemes with an increasingly higher order of accuracy for solving inviscid Euler equations. These WENO schemes firstly obtain a set of reconstruction polynomials by a hierarchy of nested central spatial stencils, and then recursively achieve a higher order approximation through the lower-order precision WENO schemes. The linear weights of such WENO schemes can be set as any positive numbers with a requirement that their sum equals one and they will not pollute the optimal order of accuracy in smooth regions and could simultaneously suppress spurious oscillations near discontinuities. Numerical results obtained indicate that these alternative finite-difference multi-resolution nested WENO schemes with different accuracies are very robust with low dissipation and use as few reconstruction stencils as possible while maintaining the same efficiency, achieving the high-resolution property without any equivalent multi-resolution representation. Besides, its finite volume form is easier to implement in unstructured grids. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=finite-difference" title="finite-difference">finite-difference</a>, <a href="https://publications.waset.org/abstracts/search?q=WENO%20schemes" title=" WENO schemes"> WENO schemes</a>, <a href="https://publications.waset.org/abstracts/search?q=high%20order" title=" high order"> high order</a>, <a href="https://publications.waset.org/abstracts/search?q=inviscid%20Euler%20equations" title=" inviscid Euler equations"> inviscid Euler equations</a>, <a href="https://publications.waset.org/abstracts/search?q=multi-resolution" title=" multi-resolution "> multi-resolution </a> </p> <a href="https://publications.waset.org/abstracts/111223/an-alternative-framework-of-multi-resolution-nested-weighted-essentially-non-oscillatory-schemes-for-solving-euler-equations-with-adaptive-order" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/111223.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">152</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">116</span> Implementation and Modeling of a Quadrotor</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ersan%20Aktas">Ersan Aktas</a>, <a href="https://publications.waset.org/abstracts/search?q=Eren%20Turano%C4%9Fuz"> Eren Turanoğuz</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this study, the quad-electrical rotor driven unmanned aerial vehicle system is designed and modeled using fundamental dynamic equations. After that, mechanical, electronical and control system of the air vehicle are designed and implemented. Brushless motor speeds are altered via electronic speed controllers in order to achieve desired controllability. The vehicle's fundamental Euler angles (i.e., roll angle, pitch angle, and yaw angle) are obtained via AHRS sensor. These angles are provided as an input to the control algorithm that run on soft the processor on the electronic card. The vehicle control algorithm is implemented in the electronic card. Controller is designed and improved for each Euler angles. Finally, flight tests have been performed to observe and improve the flight characteristics. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=quadrotor" title="quadrotor">quadrotor</a>, <a href="https://publications.waset.org/abstracts/search?q=UAS%20applications" title=" UAS applications"> UAS applications</a>, <a href="https://publications.waset.org/abstracts/search?q=control%20architectures" title=" control architectures"> control architectures</a>, <a href="https://publications.waset.org/abstracts/search?q=PID" title=" PID"> PID</a> </p> <a href="https://publications.waset.org/abstracts/48615/implementation-and-modeling-of-a-quadrotor" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/48615.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">368</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">115</span> Magnetic Survey for the Delineation of Concrete Pillars in Geotechnical Investigation for Site Characterization</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Nuraddeen%20Usman">Nuraddeen Usman</a>, <a href="https://publications.waset.org/abstracts/search?q=Khiruddin%20Abdullah"> Khiruddin Abdullah</a>, <a href="https://publications.waset.org/abstracts/search?q=Mohd%20Nawawi"> Mohd Nawawi</a>, <a href="https://publications.waset.org/abstracts/search?q=Amin%20Khalil%20Ismail"> Amin Khalil Ismail</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A magnetic survey is carried out in order to locate the remains of construction items, specifically concrete pillars. The conventional Euler deconvolution technique can perform the task but it requires the use of fixed structural index (SI) and the construction items are made of materials with different shapes which require different SI (unknown). A Euler deconvolution technique that estimate background, horizontal coordinate (xo and yo), depth and structural index (SI) simultaneously is prepared and used for this task. The synthetic model study carried indicated the new methodology can give a good estimate of location and does not depend on magnetic latitude. For field data, both the total magnetic field and gradiometer reading had been collected simultaneously. The computed vertical derivatives and gradiometer readings are compared and they have shown good correlation signifying the effectiveness of the method. The filtering is carried out using automated procedure, analytic signal and other traditional techniques. The clustered depth solutions coincided with the high amplitude/values of analytic signal and these are the possible target positions of the concrete pillars being sought. The targets under investigation are interpreted to be located at the depth between 2.8 to 9.4 meters. More follow up survey is recommended as this mark the preliminary stage of the work. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=concrete%20pillar" title="concrete pillar">concrete pillar</a>, <a href="https://publications.waset.org/abstracts/search?q=magnetic%20survey" title=" magnetic survey"> magnetic survey</a>, <a href="https://publications.waset.org/abstracts/search?q=geotechnical%20investigation" title=" geotechnical investigation"> geotechnical investigation</a>, <a href="https://publications.waset.org/abstracts/search?q=Euler%20Deconvolution" title=" Euler Deconvolution"> Euler Deconvolution</a> </p> <a href="https://publications.waset.org/abstracts/70560/magnetic-survey-for-the-delineation-of-concrete-pillars-in-geotechnical-investigation-for-site-characterization" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/70560.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">263</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">114</span> A Numerical Model Simulation for an Updraft Gasifier Using High-Temperature Steam</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=T.%20M.%20Ismail">T. M. Ismail</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20A.%20El-Salam"> M. A. El-Salam</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A mathematical model study was carried out to investigate gasification of biomass fuels using high-temperature air and steam as a gasifying agent using high-temperature air up to 1000°C. In this study, a 2D computational fluid dynamics model was developed to study the gasification process in an updraft gasifier, considering drying, pyrolysis, combustion, and gasification reactions. The gas and solid phases were resolved using a Euler−Euler multiphase approach, with exchange terms for the momentum, mass, and energy. The standard k−ε turbulence model was used in the gas phase, and the particle phase was modeled using the kinetic theory of granular flow. The results show that the present model giving a promising way in its capability and sensitivity for the parameter effects that influence the gasification process. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=computational%20fluid%20dynamics" title="computational fluid dynamics">computational fluid dynamics</a>, <a href="https://publications.waset.org/abstracts/search?q=gasification" title=" gasification"> gasification</a>, <a href="https://publications.waset.org/abstracts/search?q=biomass%20fuel" title=" biomass fuel"> biomass fuel</a>, <a href="https://publications.waset.org/abstracts/search?q=fixed%20bed%20gasifier" title=" fixed bed gasifier"> fixed bed gasifier</a> </p> <a href="https://publications.waset.org/abstracts/4947/a-numerical-model-simulation-for-an-updraft-gasifier-using-high-temperature-steam" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/4947.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">417</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">113</span> Student Project on Using a Spreadsheet for Solving Differential Equations by Euler's Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Andriy%20Didenko">Andriy Didenko</a>, <a href="https://publications.waset.org/abstracts/search?q=Zanin%20Kavazovic"> Zanin Kavazovic</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Engineering students often have certain difficulties in mastering major theoretical concepts in mathematical courses such as differential equations. Student projects were proposed to motivate students’ learning and can be used as a tool to promote students’ interest in the material. Authors propose a student project that includes the use of Microsoft Excel. This instructional tool is often overlooked by both educators and students. An integral component of the experimental part of such a project is the exploration of an interactive spreadsheet. The aim is to assist engineering students in better understanding of Euler’s method. This method is employed to numerically solve first order differential equations. At first, students are invited to select classic equations from a list presented in a form of a drop-down menu. For each of these equations, students can select and modify certain key parameters and observe the influence of initial condition on the solution. This will give students an insight into the behavior of the method in different configurations as solutions to equations are given in numerical and graphical forms. Further, students could also create their own equations by providing functions of their own choice and a variety of initial conditions. Moreover, they can visualize and explore the impact of the length of the time step on the convergence of a sequence of numerical solutions to the exact solution of the equation. As a final stage of the project, students are encouraged to develop their own spreadsheets for other numerical methods and other types of equations. Such projects promote students’ interest in mathematical applications and further improve their mathematical and programming skills. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=student%20project" title="student project">student project</a>, <a href="https://publications.waset.org/abstracts/search?q=Euler%27s%20method" title=" Euler's method"> Euler's method</a>, <a href="https://publications.waset.org/abstracts/search?q=spreadsheet" title=" spreadsheet"> spreadsheet</a>, <a href="https://publications.waset.org/abstracts/search?q=engineering%20education" title=" engineering education"> engineering education</a> </p> <a href="https://publications.waset.org/abstracts/112422/student-project-on-using-a-spreadsheet-for-solving-differential-equations-by-eulers-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/112422.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">137</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">112</span> Analysis of Transverse Vibrations in Uniform Beams Subject to Different End Restraints</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Falek%20Kamel">Falek Kamel</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Free vibration analysis of beams, based on the assumptions of Bernoulli-Euler theory, has been extensively studied. Many research works have focused on the study of transverse vibrations under the application of different boundary conditions where different theories have been applied. The stiffness and mass matrices considered are those obtained by assembling those resulting from the use of the finite element method. The Jacobi method has been used to solve the eigenvalue problem. These well-known concepts have been applied to the study of beams with constant geometric and mechanical characteristics having one to two overhangs with variable lengths. Murphy studied, by an algebraic solution approach, a simply supported beam with two overhangs of arbitrary length, allowing for an experimental determination of the elastic modulus E. The advantage of our article is that it offers the possibility of extending this approach to many interesting problems formed by transversely vibrating beams with various end constraints. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=beam" title="beam">beam</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20element" title=" finite element"> finite element</a>, <a href="https://publications.waset.org/abstracts/search?q=transverse%20vibrations" title=" transverse vibrations"> transverse vibrations</a>, <a href="https://publications.waset.org/abstracts/search?q=end%20restreint" title=" end restreint"> end restreint</a>, <a href="https://publications.waset.org/abstracts/search?q=Bernoulli-Euler%20theory" title=" Bernoulli-Euler theory"> Bernoulli-Euler theory</a> </p> <a href="https://publications.waset.org/abstracts/163630/analysis-of-transverse-vibrations-in-uniform-beams-subject-to-different-end-restraints" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/163630.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">90</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">111</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">396</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">110</span> C Vibration Analysis of a Beam on Elastic Foundation with Elastically Restrained Ends Using Spectral Element Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hamioud%20Saida">Hamioud Saida</a>, <a href="https://publications.waset.org/abstracts/search?q=Khalfallah%20Salah"> Khalfallah Salah</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this study, a spectral element method is employed to predict the free vibration of a Euler-Bernoulli beam resting on a Winkler foundation with elastically restrained ends. The formulation of the dynamic stiffness matrix has been established by solving the differential equation of motion, which was transformed to frequency domain. Non-dimensional natural frequencies and shape modes are obtained by solving the partial differential equations, numerically. Numerical comparisons and examples are performed to show the effectiveness of the SEM and to investigate the effects of various parameters, such as the springs at the boundaries and the elastic foundation parameter on the vibration frequencies. The obtained results demonstrate that the present method can also be applied to solve the more general problem of the dynamic analysis of structures with higher order precision. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=elastically%20supported%20Euler-Bernoulli%20beam" title="elastically supported Euler-Bernoulli beam">elastically supported Euler-Bernoulli beam</a>, <a href="https://publications.waset.org/abstracts/search?q=free-vibration" title=" free-vibration"> free-vibration</a>, <a href="https://publications.waset.org/abstracts/search?q=spectral%20element%20method" title=" spectral element method"> spectral element method</a>, <a href="https://publications.waset.org/abstracts/search?q=Winkler%20foundation" title=" Winkler foundation"> Winkler foundation</a> </p> <a href="https://publications.waset.org/abstracts/110401/c-vibration-analysis-of-a-beam-on-elastic-foundation-with-elastically-restrained-ends-using-spectral-element-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/110401.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">136</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">109</span> Numerical Simulation of Wishart Diffusion Processes</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Raphael%20Naryongo">Raphael Naryongo</a>, <a href="https://publications.waset.org/abstracts/search?q=Philip%20%20Ngare"> Philip Ngare</a>, <a href="https://publications.waset.org/abstracts/search?q=Anthony%20%20Waititu"> Anthony Waititu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper deals with numerical simulation of Wishart processes for a single asset risky pricing model whose volatility is described by Wishart affine diffusion processes. The multi-factor specification of volatility will make the model more flexible enough to fit the stock market data for short or long maturities for better returns. The Wishart process is a stochastic process which is a positive semi-definite matrix-valued generalization of the square root process. The aim of the study is to model the log asset stock returns under the double Wishart stochastic volatility model. The solution of the log-asset return dynamics for Bi-Wishart processes will be obtained through Euler-Maruyama discretization schemes. The numerical results on the asset returns are compared to the existing models returns such as Heston stochastic volatility model and double Heston stochastic volatility model <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=euler%20schemes" title="euler schemes">euler schemes</a>, <a href="https://publications.waset.org/abstracts/search?q=log-asset%20return" title=" log-asset return"> log-asset return</a>, <a href="https://publications.waset.org/abstracts/search?q=infinitesimal%20generator" title=" infinitesimal generator"> infinitesimal generator</a>, <a href="https://publications.waset.org/abstracts/search?q=wishart%20diffusion%20affine%20processes" title=" wishart diffusion affine processes "> wishart diffusion affine processes </a> </p> <a href="https://publications.waset.org/abstracts/137631/numerical-simulation-of-wishart-diffusion-processes" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/137631.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">388</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">108</span> An Inviscid Compressible Flow Solver Based on Unstructured OpenFOAM Mesh Format</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Utkan%20Caliskan">Utkan Caliskan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Two types of numerical codes based on finite volume method are developed in order to solve compressible Euler equations to simulate the flow through forward facing step channel. Both algorithms have AUSM+- up (Advection Upstream Splitting Method) scheme for flux splitting and two-stage Runge-Kutta scheme for time stepping. In this study, the flux calculations differentiate between the algorithm based on OpenFOAM mesh format which is called 'face-based' algorithm and the basic algorithm which is called 'element-based' algorithm. The face-based algorithm avoids redundant flux computations and also is more flexible with hybrid grids. Moreover, some of OpenFOAM’s preprocessing utilities can be used on the mesh. Parallelization of the face based algorithm for which atomic operations are needed due to the shared memory model, is also presented. For several mesh sizes, 2.13x speed up is obtained with face-based approach over the element-based approach. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=cell%20centered%20finite%20volume%20method" title="cell centered finite volume method">cell centered finite volume method</a>, <a href="https://publications.waset.org/abstracts/search?q=compressible%20Euler%20equations" title=" compressible Euler equations"> compressible Euler equations</a>, <a href="https://publications.waset.org/abstracts/search?q=OpenFOAM%20mesh%20format" title=" OpenFOAM mesh format"> OpenFOAM mesh format</a>, <a href="https://publications.waset.org/abstracts/search?q=OpenMP" title=" OpenMP"> OpenMP</a> </p> <a href="https://publications.waset.org/abstracts/73005/an-inviscid-compressible-flow-solver-based-on-unstructured-openfoam-mesh-format" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/73005.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">107</span> Delineating Subsurface Linear Features and Faults Under Sedimentary Cover in the Bahira Basin Using Integrated Gravity and Magnetic Data</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20Lghoul">M. Lghoul</a>, <a href="https://publications.waset.org/abstracts/search?q=N.%20El%20Goumi"> N. El Goumi</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20Guernouche"> M. Guernouche</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In order to predict the structural and tectonic framework of the Bahira basin and to have a 3D geological modeling of the basin, an integrated multidisciplinary work has been conducted using gravity, magnetic and geological data. The objective of the current study is delineating the subsurfacefeatures, faults, and geological limits, using airborne magnetic and gravity data analysis of the Bahira basin. To achieve our goal, we have applied different enhanced techniques on magnetic and gravity data: power spectral analysis techniques, reduction to pole (RTP), upward continuation, analytical signal, tilt derivative, total horizontal derivative, 3D Euler deconvolutionand source parameter imagining. The major lineaments/faults trend are: NE–SW, NW-SE, ENE–WSW, and WNW–ESE. The 3D Euler deconvolution analysis highlighted a number of fault trend, mainly in the ENE-WSW, WNW-ESE directions. The depth tothe top of the basement sources in the study area ranges between 200 m, in the southern and northern part of the Bahira basin, to 5000 m located in the Eastern part of the basin. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=magnetic" title="magnetic">magnetic</a>, <a href="https://publications.waset.org/abstracts/search?q=gravity" title=" gravity"> gravity</a>, <a href="https://publications.waset.org/abstracts/search?q=structural%20trend" title=" structural trend"> structural trend</a>, <a href="https://publications.waset.org/abstracts/search?q=depth%20to%20basement" title=" depth to basement"> depth to basement</a> </p> <a href="https://publications.waset.org/abstracts/147461/delineating-subsurface-linear-features-and-faults-under-sedimentary-cover-in-the-bahira-basin-using-integrated-gravity-and-magnetic-data" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/147461.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">137</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">106</span> A Combined Error Control with Forward Euler Method for Dynamical Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=R.%20Vigneswaran">R. Vigneswaran</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20Thilakanathan"> S. Thilakanathan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Variable time-stepping algorithms for solving dynamical systems performed poorly for long time computations which pass close to a fixed point. To overcome this difficulty, several authors considered phase space error controls for numerical simulation of dynamical systems. In one generalized phase space error control, a step-size selection scheme was proposed, which allows this error control to be incorporated into the standard adaptive algorithm as an extra constraint at negligible extra computational cost. For this generalized error control, it was already analyzed the forward Euler method applied to the linear system whose coefficient matrix has real and negative eigenvalues. In this paper, this result was extended to the linear system whose coefficient matrix has complex eigenvalues with negative real parts. Some theoretical results were obtained and numerical experiments were carried out to support the theoretical results. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=adaptivity" title="adaptivity">adaptivity</a>, <a href="https://publications.waset.org/abstracts/search?q=fixed%20point" title=" fixed point"> fixed point</a>, <a href="https://publications.waset.org/abstracts/search?q=long%20time%20simulations" title=" long time simulations"> long time simulations</a>, <a href="https://publications.waset.org/abstracts/search?q=stability" title=" stability"> stability</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20system" title=" linear system"> linear system</a> </p> <a href="https://publications.waset.org/abstracts/48246/a-combined-error-control-with-forward-euler-method-for-dynamical-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/48246.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">319</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">105</span> Investigation of Steel-Concrete Composite Bridges under Blasting Loads Based on Slope Reflection</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yuan%20Li">Yuan Li</a>, <a href="https://publications.waset.org/abstracts/search?q=Yitao%20Han"> Yitao Han</a>, <a href="https://publications.waset.org/abstracts/search?q=Zhao%20Zhu"> Zhao Zhu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, the effect of blasting loads on steel-concrete composite bridges has been investigated considering the slope reflection effect. Reasonable values of girder size, plate thickness, stiffening rib, and other design parameters were selected according to design specifications. Modified RHT (Riedel-Hiermaier-Thoma) was used as constitutive relation in analyses. In order to simulate the slope reflection effect, the slope of the bridge was precisely built in the model. Different blasting conditions, including top, middle, and bottom explosions, were simulated. The multi-Euler domain method based on fully coupled Lagrange and Euler models was adopted for the structural analysis of the explosion process using commercial software AUTODYN. The obtained results showed that explosion overpressure was increased by 3006, 879, and 449kPa, corresponding to explosions occurring at the top, middle, and bottom of the slope, respectively. At the same time, due to energy accumulation and transmission dissipation caused by slope reflection, the corresponding yield lengths of steel beams were increased by 8, 0, and 5m, respectively. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=steel-concrete%20composite%20bridge" title="steel-concrete composite bridge">steel-concrete composite bridge</a>, <a href="https://publications.waset.org/abstracts/search?q=explosion%20damage" title=" explosion damage"> explosion damage</a>, <a href="https://publications.waset.org/abstracts/search?q=slope%20reflection" title=" slope reflection"> slope reflection</a>, <a href="https://publications.waset.org/abstracts/search?q=blasting%20loads" title=" blasting loads"> blasting loads</a>, <a href="https://publications.waset.org/abstracts/search?q=RHT" title=" RHT"> RHT</a> </p> <a href="https://publications.waset.org/abstracts/150132/investigation-of-steel-concrete-composite-bridges-under-blasting-loads-based-on-slope-reflection" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/150132.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">99</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">104</span> A Study on Mesh Size Dependency on Bed Expansion Zone in a Three-Phase Fluidized Bed Reactor</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Liliana%20Patricia%20Olivo%20Arias">Liliana Patricia Olivo Arias</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The present study focused on the hydrodynamic study in a three-phase fluidized bed reactor and the influence of important aspects, such as volume fractions (Hold up), velocity magnitude of gas, liquid and solid phases (hydrogen, gasoil, and gamma alumina), interactions of phases, through of drag models with the k-epsilon turbulence model. For this purpose was employed a Euler-Euler model and also considers the system is constituted of three phases, gaseous, liquid and solid, characterized by its physical and thermal properties, the transport processes that are developed within the transient regime. The proposed model of the three-phase fluidized bed reactor was solved numerically using the ANSYS-Fluent software with different mesh refinements on bed expansion zone in order to observe the influence of the hydrodynamic parameters and convergence criteria. With this model and the numerical simulations obtained for its resolution, it was possible to predict the results of the volume fractions (Hold ups) and the velocity magnitude for an unsteady system from the initial and boundaries conditions were established. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=three-phase%20fluidized%20bed%20system" title="three-phase fluidized bed system">three-phase fluidized bed system</a>, <a href="https://publications.waset.org/abstracts/search?q=CFD%20simulation" title=" CFD simulation"> CFD simulation</a>, <a href="https://publications.waset.org/abstracts/search?q=mesh%20dependency%20study" title=" mesh dependency study"> mesh dependency study</a>, <a href="https://publications.waset.org/abstracts/search?q=hydrodynamic%20study" title=" hydrodynamic study"> hydrodynamic study</a> </p> <a href="https://publications.waset.org/abstracts/93603/a-study-on-mesh-size-dependency-on-bed-expansion-zone-in-a-three-phase-fluidized-bed-reactor" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/93603.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">172</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">103</span> Kirchoff Type Equation Involving the p-Laplacian on the Sierpinski Gasket Using Nehari Manifold Technique</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Abhilash%20Sahu">Abhilash Sahu</a>, <a href="https://publications.waset.org/abstracts/search?q=Amit%20Priyadarshi"> Amit Priyadarshi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we will discuss the existence of weak solutions of the Kirchhoff type boundary value problem on the Sierpinski gasket. Where S denotes the Sierpinski gasket in R² and S₀ is the intrinsic boundary of the Sierpinski gasket. M: R → R is a positive function and h: S × R → R is a suitable function which is a part of our main equation. ∆p denotes the p-Laplacian, where p > 1. First of all, we will define a weak solution for our problem and then we will show the existence of at least two solutions for the above problem under suitable conditions. There is no well-known concept of a generalized derivative of a function on a fractal domain. Recently, the notion of differential operators such as the Laplacian and the p-Laplacian on fractal domains has been defined. We recall the result first then we will address the above problem. In view of literature, Laplacian and p-Laplacian equations are studied extensively on regular domains (open connected domains) in contrast to fractal domains. In fractal domains, people have studied Laplacian equations more than p-Laplacian probably because in that case, the corresponding function space is reflexive and many minimax theorems which work for regular domains is applicable there which is not the case for the p-Laplacian. This motivates us to study equations involving p-Laplacian on the Sierpinski gasket. Problems on fractal domains lead to nonlinear models such as reaction-diffusion equations on fractals, problems on elastic fractal media and fluid flow through fractal regions etc. We have studied the above p-Laplacian equations on the Sierpinski gasket using fibering map technique on the Nehari manifold. Many authors have studied the Laplacian and p-Laplacian equations on regular domains using this Nehari manifold technique. In general Euler functional associated with such a problem is Frechet or Gateaux differentiable. So, a critical point becomes a solution to the problem. Also, the function space they consider is reflexive and hence we can extract a weakly convergent subsequence from a bounded sequence. But in our case neither the Euler functional is differentiable nor the function space is known to be reflexive. Overcoming these issues we are still able to prove the existence of at least two solutions of the given equation. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Euler%20functional" title="Euler functional">Euler functional</a>, <a href="https://publications.waset.org/abstracts/search?q=p-Laplacian" title=" p-Laplacian"> p-Laplacian</a>, <a href="https://publications.waset.org/abstracts/search?q=p-energy" title=" p-energy"> p-energy</a>, <a href="https://publications.waset.org/abstracts/search?q=Sierpinski%20gasket" title=" Sierpinski gasket"> Sierpinski gasket</a>, <a href="https://publications.waset.org/abstracts/search?q=weak%20solution" title=" weak solution"> weak solution</a> </p> <a href="https://publications.waset.org/abstracts/89044/kirchoff-type-equation-involving-the-p-laplacian-on-the-sierpinski-gasket-using-nehari-manifold-technique" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/89044.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">239</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=Euler&page=2">2</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=Euler&page=3">3</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=Euler&page=4">4</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=Euler&page=5">5</a></li> <li class="page-item"><a class="page-link" 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