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Search results for: finite-difference beam propagation method
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class="card"> <div class="card-body"><strong>Paper Count:</strong> 20050</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: finite-difference beam propagation method</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">20050</span> Propagation of Cos-Gaussian Beam in Photorefractive Crystal</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> </p> <p class="card-text"><strong>Abstract:</strong></p> A physical model for guiding the wave in photorefractive media is studied. Propagation of cos-Gaussian beam as the special cases of sinusoidal-Gaussian beams in photorefractive crystal is simulated numerically by the Crank-Nicolson method in one dimension. Results show that the beam profile deforms as the energy transfers from the center to the tails under propagation. This simulation approach is of significant interest for application in optical telecommunication. The results are presented graphically and discussed. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=beam%20propagation" title="beam propagation">beam propagation</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=numerical%20simulation" title=" numerical simulation"> numerical simulation</a>, <a href="https://publications.waset.org/abstracts/search?q=photorefractive%20crystal" title=" photorefractive crystal"> photorefractive crystal</a> </p> <a href="https://publications.waset.org/abstracts/33883/propagation-of-cos-gaussian-beam-in-photorefractive-crystal" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/33883.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">499</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">20049</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">20048</span> The Cracks Propagation Monitoring of a Cantilever Beam Using Modal Analysis </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Morteza%20Raki">Morteza Raki</a>, <a href="https://publications.waset.org/abstracts/search?q=Abolghasem%20Zabihollah"> Abolghasem Zabihollah</a>, <a href="https://publications.waset.org/abstracts/search?q=Omid%20Askari"> Omid Askari </a> </p> <p class="card-text"><strong>Abstract:</strong></p> Cantilever beam is a simplified sample of a lot of mechanical components used in a wide range of applications, including many industries such as gas turbine blade. Due to the nature of the operating conditions, beams are subject to variety of damages especially crack propagates. Crack propagation may lead to catastrophic failure during operation. Therefore, online detection of crack presence and its propagation is very important and may reduce possible significant cost of the whole system failure. This paper aims to investigate the effect of cracks presence and crack propagation on one end fixed beam`s vibration. A finite element model will be developed for the blade in which the modal response of the structure with and without crack will be studied. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=blade" title="blade">blade</a>, <a href="https://publications.waset.org/abstracts/search?q=crack%20propagation" title=" crack propagation"> crack propagation</a>, <a href="https://publications.waset.org/abstracts/search?q=health%20monitoring" title=" health monitoring"> health monitoring</a>, <a href="https://publications.waset.org/abstracts/search?q=modal%20analysis" title=" modal analysis"> modal analysis</a> </p> <a href="https://publications.waset.org/abstracts/48812/the-cracks-propagation-monitoring-of-a-cantilever-beam-using-modal-analysis" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/48812.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">20047</span> Numerical Simulation of Laser Propagation through Turbulent Atmosphere Using Zernike Polynomials</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohammad%20Moradi%20%E2%80%8E">Mohammad Moradi </a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this article, propagation of a laser beam through turbulent atmosphere is evaluated. At first the laser beam is simulated and then turbulent atmosphere will be simulated by using Zernike polynomials. Some parameter like intensity, PSF will be measured for four wavelengths in different Cn2. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=laser%20beam%20propagation" title="laser beam propagation">laser beam propagation</a>, <a href="https://publications.waset.org/abstracts/search?q=phase%20screen" title=" phase screen"> phase screen</a>, <a href="https://publications.waset.org/abstracts/search?q=turbulent%20atmosphere" title=" turbulent atmosphere"> turbulent atmosphere</a>, <a href="https://publications.waset.org/abstracts/search?q=Zernike%20%E2%80%8Epolynomials" title=" Zernike polynomials"> Zernike polynomials</a> </p> <a href="https://publications.waset.org/abstracts/35907/numerical-simulation-of-laser-propagation-through-turbulent-atmosphere-using-zernike-polynomials" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/35907.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">511</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">20046</span> Analysis of Nonlinear Pulse Propagation Characteristics in Semiconductor Optical Amplifier for Different Input Pulse Shapes</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Suchi%20Barua">Suchi Barua</a>, <a href="https://publications.waset.org/abstracts/search?q=Narottam%20Das"> Narottam Das</a>, <a href="https://publications.waset.org/abstracts/search?q=Sven%20Nordholm"> Sven Nordholm</a>, <a href="https://publications.waset.org/abstracts/search?q=Mohammad%20Razaghi"> Mohammad Razaghi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents nonlinear pulse propagation characteristics for different input optical pulse shapes with various input pulse energy levels in semiconductor optical amplifiers. For simulation of nonlinear pulse propagation, finite-difference beam propagation method is used to solve the nonlinear Schrödinger equation. In this equation, gain spectrum dynamics, gain saturation are taken into account which depends on carrier depletion, carrier heating, spectral-hole burning, group velocity dispersion, self-phase modulation and two photon absorption. From this analysis, we obtained the output waveforms and spectra for different input pulse shapes as well as for different input energies. It shows clearly that the peak position of the output waveforms are shifted toward the leading edge which due to the gain saturation of the SOA for higher input pulse energies. We also analyzed and compared the normalized difference of full-width at half maximum for different input pulse shapes in the SOA. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=finite-difference%20beam%20propagation%20method" title="finite-difference beam propagation method">finite-difference beam propagation method</a>, <a href="https://publications.waset.org/abstracts/search?q=pulse%20shape" title=" pulse shape"> pulse shape</a>, <a href="https://publications.waset.org/abstracts/search?q=pulse%20propagation" title=" pulse propagation"> pulse propagation</a>, <a href="https://publications.waset.org/abstracts/search?q=semiconductor%20optical%20amplifier" title=" semiconductor optical amplifier"> semiconductor optical amplifier</a> </p> <a href="https://publications.waset.org/abstracts/20730/analysis-of-nonlinear-pulse-propagation-characteristics-in-semiconductor-optical-amplifier-for-different-input-pulse-shapes" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/20730.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">607</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">20045</span> Numerical Analysis of Shear Crack Propagation in a Concrete Beam without Transverse Reinforcement</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=G.%20A.%20Rombach">G. A. Rombach</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20Faron"> A. Faron</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Crack formation and growth in reinforced concrete members are, in many cases, the cause of the collapse of technical structures. Such serious failures impair structural behavior and can also damage property and persons. An intensive investigation of the crack propagation is indispensable. Numerical methods are being developed to analyze crack growth in an element and to detect fracture failure at an early stage. For reinforced concrete components, however, further research and action are required in the analysis of shear cracks. This paper presents numerical simulations and continuum mechanical modeling of bending shear crack propagation in a three-dimensional reinforced concrete beam without transverse reinforcement. The analysis will provide a further understanding of crack growth and redistribution of inner forces in concrete members. As a numerical method to map discrete cracks, the extended finite element method (XFEM) is applied. The crack propagation is compared with the smeared crack approach using concrete damage plasticity. For validation, the crack patterns of real experiments are compared with the results of the different finite element models. The evaluation is based on single span beams under bending. With the analysis, it is possible to predict the fracture behavior of concrete members. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=concrete%20damage%20plasticity" title="concrete damage plasticity">concrete damage plasticity</a>, <a href="https://publications.waset.org/abstracts/search?q=crack%20propagation" title=" crack propagation"> crack propagation</a>, <a href="https://publications.waset.org/abstracts/search?q=extended%20finite%20element%20method" title=" extended finite element method"> extended finite element method</a>, <a href="https://publications.waset.org/abstracts/search?q=fracture%20mechanics" title=" fracture mechanics"> fracture mechanics</a> </p> <a href="https://publications.waset.org/abstracts/105887/numerical-analysis-of-shear-crack-propagation-in-a-concrete-beam-without-transverse-reinforcement" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/105887.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">119</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">20044</span> Crack Propagation Effect at the Interface of a Composite Beam</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mezidi%20Amar">Mezidi Amar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this research work, crack propagation at the interface of a composite beam is considered. The behavior of composite beams (CB) depends upon a law based on relationship between tangential or normal efforts with inelastic propagation. Throughout this study, composite beams are classified like composite beams with partial connection or sandwich beams of three layers. These structural systems are controlled by the same nature of differential equations regarding their behavior in the plane, as well as out-of-plane. Multi-layer elements with partial connection are typically met in the field of timber construction where the elements are assembled by joining. The formalism of the behavior in the plane and out-of-plane of these composite beams is obtained and their results concerning the engineering aspect or simple of interpretation are proposed for the case of composite beams made up of rectangular section and simply supported section. An apparent analytical peculiarity or paradox in the bending behavior of elastic–composite beams with interlayer slip, sandwich beam or other similar problems subjected to boundary moments exists. For a fully composite beam subjected to end moments, the partial composite model will render a non-vanishing uniform value for the normal force in the individual subelement. Obtained results are similar to those for the case of vibrations in the plane as well for the composite beams as for the sandwich beams where eigen-frequencies increase with related rigidity. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=composite%20beam" title="composite beam">composite beam</a>, <a href="https://publications.waset.org/abstracts/search?q=behaviour" title=" behaviour"> behaviour</a>, <a href="https://publications.waset.org/abstracts/search?q=interface" title=" interface"> interface</a>, <a href="https://publications.waset.org/abstracts/search?q=deflection" title=" deflection"> deflection</a>, <a href="https://publications.waset.org/abstracts/search?q=propagation" title=" propagation"> propagation</a> </p> <a href="https://publications.waset.org/abstracts/44240/crack-propagation-effect-at-the-interface-of-a-composite-beam" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/44240.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">300</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">20043</span> Beam Methods Applications to the Design of Curved Pulsed Beams</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Timor%20Melamed">Timor Melamed</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this study, we consider two methods for synthesizing a pulsed curved beam along a generic beam-axis trajectory. In the first approach, we evaluate the space-time aperture field distribution that radiates the beam along a predefined trajectory by constructing a time-dependent caustic surface around the beam-axis skeleton. We derive the aperture field delay to form a caustic of rays along the beam axis and extend this method to other points over the aperture. In the second approach, we harness the proven capabilities of beam methods to address the challenge of designing curved intensity profiles in three-dimensional free space. By leveraging advanced beam propagation techniques, we create and manipulate complex intensity patterns along arbitrarily curved trajectories, offering additional possibilities for precision control in various wave-based applications. Numerical examples are presented to demonstrate the robust capabilities of both methods. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=pulsed%20Airy%20beams" title="pulsed Airy beams">pulsed Airy beams</a>, <a href="https://publications.waset.org/abstracts/search?q=pulsed%20beams" title=" pulsed beams"> pulsed beams</a>, <a href="https://publications.waset.org/abstracts/search?q=pulsed%20curved%20beams" title=" pulsed curved beams"> pulsed curved beams</a>, <a href="https://publications.waset.org/abstracts/search?q=transient%20fields" title=" transient fields"> transient fields</a> </p> <a href="https://publications.waset.org/abstracts/192271/beam-methods-applications-to-the-design-of-curved-pulsed-beams" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/192271.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">22</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">20042</span> The Beam Expansion Method, A Simplified and Efficient Approach of Field Propagation and Resonators Modes Study</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Zaia%20Derrar%20Kaddour">Zaia Derrar Kaddour</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The study of a beam throughout an optical path is generally achieved by means of diffraction integral. Unfortunately, in some problems, this tool turns out to be not very friendly and hard to implement. Instead, the beam expansion method for computing field profiles appears to be an interesting alternative. The beam expansion method consists of expanding the field pattern as a series expansion in a set of orthogonal functions. Propagating each individual component through a circuit and adding up the derived elements leads easily to the result. The problem is then reduced to finding how the expansion coefficients change in a circuit. The beam expansion method requires a systematic study of each type of optical element that can be met in the considered optical path. In this work, we analyze the following fundamental elements: first order optical systems, hard apertures and waveguides. We show that the former element type is completely defined thanks to the Gouy phase shift expression we provide and the latters require a suitable mode conversion. For endorsing the usefulness and relevance of the beam expansion approach, we show here some of its applications such as the treatment of the thermal lens effect and the study of unstable resonators. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=gouy%20phase%20shift" title="gouy phase shift">gouy phase shift</a>, <a href="https://publications.waset.org/abstracts/search?q=modes" title=" modes"> modes</a>, <a href="https://publications.waset.org/abstracts/search?q=optical%20resonators" title=" optical resonators"> optical resonators</a>, <a href="https://publications.waset.org/abstracts/search?q=unstable%20resonators" title=" unstable resonators"> unstable resonators</a> </p> <a href="https://publications.waset.org/abstracts/181610/the-beam-expansion-method-a-simplified-and-efficient-approach-of-field-propagation-and-resonators-modes-study" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/181610.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">62</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">20041</span> Compact Low Loss Design of SOI 1x2 Y-Branch Optical Power Splitter with S-Bend Waveguide and Study on the Variation of Transmitted Power with Various Waveguide Parameters</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Nagaraju%20Pendam">Nagaraju Pendam</a>, <a href="https://publications.waset.org/abstracts/search?q=C.%20P.%20Vardhani"> C. P. Vardhani</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A simple technology–compatible design of silicon-on-insulator based 1×2 optical power splitter is proposed. For developing large area Opto-electronic Silicon-on-Insulator (SOI) devices, the power splitter is a key passive device. The SOI rib- waveguide dimensions (height, width, and etching depth, refractive indices, length of waveguide) leading simultaneously to single mode propagation. In this paper a low loss optical power splitter is designed by using R Soft cad tool and simulated by Beam propagation method, here s-bend waveguides proposed. We concentrate changing the refractive index difference, branching angle, width of the waveguide, free space wavelength of the waveguide and observing transmitted power, effective refractive index in the designed waveguide, and choosing the best simulated results to be fabricated on silicon-on insulator platform. In this design 1550 nm free spacing are used. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=beam%20propagation%20method" title="beam propagation method">beam propagation method</a>, <a href="https://publications.waset.org/abstracts/search?q=insertion%20loss" title=" insertion loss"> insertion loss</a>, <a href="https://publications.waset.org/abstracts/search?q=optical%20power%20splitter" title=" optical power splitter"> optical power splitter</a>, <a href="https://publications.waset.org/abstracts/search?q=rib%20waveguide" title=" rib waveguide"> rib waveguide</a>, <a href="https://publications.waset.org/abstracts/search?q=transmitted%20power" title=" transmitted power"> transmitted power</a> </p> <a href="https://publications.waset.org/abstracts/16984/compact-low-loss-design-of-soi-1x2-y-branch-optical-power-splitter-with-s-bend-waveguide-and-study-on-the-variation-of-transmitted-power-with-various-waveguide-parameters" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/16984.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">663</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">20040</span> Self-Action Effects of a Non-Gaussian Laser Beam Through Plasma </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sandeep%20Kumar">Sandeep Kumar</a>, <a href="https://publications.waset.org/abstracts/search?q=Naveen%20Gupta"> Naveen Gupta</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The propagation of the Non-Gaussian laser beam results in strong self-focusing as compare to the Gaussian laser beam, which helps to achieve a prerequisite of the plasma-based electron, Terahertz generation, and higher harmonic generations. The theoretical investigation on the evolution of non-Gaussian laser beam through the collisional plasma with ramped density has been presented. The non-uniform irradiance over the cross-section of the laser beam results in redistribution of the carriers that modifies the optical response of the plasma in such a way that the plasma behaves like a converging lens to the laser beam. The formulation is based on finding a semi-analytical solution of the nonlinear Schrodinger wave equation (NLSE) with the help of variational theory. It has been observed that the decentred parameter ‘q’ of laser and wavenumber of ripples of medium contribute to providing the required conditions for the improvement of self-focusing. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=non-Gaussian%20beam" title="non-Gaussian beam">non-Gaussian beam</a>, <a href="https://publications.waset.org/abstracts/search?q=collisional%20plasma" title=" collisional plasma"> collisional plasma</a>, <a href="https://publications.waset.org/abstracts/search?q=variational%20theory" title=" variational theory"> variational theory</a>, <a href="https://publications.waset.org/abstracts/search?q=self-focusing" title=" self-focusing"> self-focusing</a> </p> <a href="https://publications.waset.org/abstracts/124754/self-action-effects-of-a-non-gaussian-laser-beam-through-plasma" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/124754.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">195</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">20039</span> Analysis of 3 dB Directional Coupler Based On Silicon-On-Insulator (SOI) Large Cross-Section Rib Waveguide</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Nurdiani%20Zamhari">Nurdiani Zamhari</a>, <a href="https://publications.waset.org/abstracts/search?q=Abang%20Annuar%20Ehsan"> Abang Annuar Ehsan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The 3 dB directional coupler is designed by using silicon-on-insulator (SOI) large cross-section and simulate by Beam Propagation Method at the communication wavelength of 1.55 µm and 1.48 µm. The geometry is shaped with rib height (H) of 6 µm and varied in step factor (r) which is 0.5, 0.6, 0.7 and 0.8. The wave guide spacing is also fixed to 5 µm and the slab width is symmetrical. In general, the 3 dB coupling lengths for four different cross-sections are several millimetre long. The 1.48 of wavelength give the longer coupling length if compare to 1.55 at the same step factor (r). Besides, the low loss propagation is achieved with less than 2 % of propagation loss. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=3%20dB%20directional%20couplers" title="3 dB directional couplers">3 dB directional couplers</a>, <a href="https://publications.waset.org/abstracts/search?q=silicon-on-insulator" title=" silicon-on-insulator"> silicon-on-insulator</a>, <a href="https://publications.waset.org/abstracts/search?q=symmetrical%20rib%20waveguide" title=" symmetrical rib waveguide"> symmetrical rib waveguide</a>, <a href="https://publications.waset.org/abstracts/search?q=OptiBPM%209" title=" OptiBPM 9 "> OptiBPM 9 </a> </p> <a href="https://publications.waset.org/abstracts/19712/analysis-of-3-db-directional-coupler-based-on-silicon-on-insulator-soi-large-cross-section-rib-waveguide" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/19712.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">516</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">20038</span> Super Harmonic Nonlinear Lateral Vibration of an Axially Moving Beam with Rotating Prismatic Joint</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20Najafi">M. Najafi</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20Bab"> S. Bab</a>, <a href="https://publications.waset.org/abstracts/search?q=F.%20Rahimi%20Dehgolan"> F. Rahimi Dehgolan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The motion of an axially moving beam with rotating prismatic joint with a tip mass on the end is analyzed to investigate the nonlinear vibration and dynamic stability of the beam. The beam is moving with a harmonic axially and rotating velocity about a constant mean velocity. A time-dependent partial differential equation and boundary conditions with the aid of the Hamilton principle are derived to describe the beam lateral deflection. After the partial differential equation is discretized by the Galerkin method, the method of multiple scales is applied to obtain analytical solutions. Frequency response curves are plotted for the super harmonic resonances of the first and the second modes. The effects of non-linear term and mean velocity are investigated on the steady state response of the axially moving beam. The results are validated with numerical simulations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=super%20harmonic%20resonances" title="super harmonic resonances">super harmonic resonances</a>, <a href="https://publications.waset.org/abstracts/search?q=non-linear%20vibration" title=" non-linear vibration"> non-linear vibration</a>, <a href="https://publications.waset.org/abstracts/search?q=axially%20moving%20beam" title=" axially moving beam"> axially moving beam</a>, <a href="https://publications.waset.org/abstracts/search?q=Galerkin%20method" title=" Galerkin method"> Galerkin method</a> </p> <a href="https://publications.waset.org/abstracts/67098/super-harmonic-nonlinear-lateral-vibration-of-an-axially-moving-beam-with-rotating-prismatic-joint" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/67098.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">391</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">20037</span> Vibration Control of a Functionally Graded Carbon Nanotube-Reinforced Composites Beam Resting on Elastic Foundation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Gholamhosein%20Khosravi">Gholamhosein Khosravi</a>, <a href="https://publications.waset.org/abstracts/search?q=Mohammad%20Azadi"> Mohammad Azadi</a>, <a href="https://publications.waset.org/abstracts/search?q=Hamidreza%20Ghezavati"> Hamidreza Ghezavati</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, vibration of a nonlinear composite beam is analyzed and then an active controller is used to control the vibrations of the system. The beam is resting on a Winkler-Pasternak elastic foundation. The composite beam is reinforced by single walled carbon nanotubes. Using the rule of mixture, the material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTRCs) are determined. The beam is cantilever and the free end of the beam is under follower force. Piezoelectric layers are attached to the both sides of the beam to control vibrations as sensors and actuators. The governing equations of the FG-CNTRC beam are derived based on Euler-Bernoulli beam theory Lagrange- Rayleigh-Ritz method. The simulation results are presented and the effects of some parameters on stability of the beam are analyzed. <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=vibration%20control" title=" vibration control"> vibration control</a>, <a href="https://publications.waset.org/abstracts/search?q=piezoelectric%20layers" title=" piezoelectric layers"> piezoelectric layers</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/53457/vibration-control-of-a-functionally-graded-carbon-nanotube-reinforced-composites-beam-resting-on-elastic-foundation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/53457.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">270</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">20036</span> Ray Tracing Modified 3D Image Method Simulation of Picocellular Propagation Channel Environment</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Fathi%20Alwafie">Fathi Alwafie</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper we present the simulation of the propagation characteristics of the picocellular propagation channel environment. The first aim has been to find a correct description of the environment for received wave. The result of the first investigations is that the environment of the indoor wave significantly changes as we change the electric parameters of material constructions. A modified 3D ray tracing image method tool has been utilized for the coverage prediction. A detailed analysis of the dependence of the indoor wave on the wide-band characteristics of the channel: Root Mean Square (RMS) delay spread characteristics and mean excess delay, is also investigated. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=propagation" title="propagation">propagation</a>, <a href="https://publications.waset.org/abstracts/search?q=ray%20tracing" title=" ray tracing"> ray tracing</a>, <a href="https://publications.waset.org/abstracts/search?q=network" title=" network"> network</a>, <a href="https://publications.waset.org/abstracts/search?q=mobile%20computing" title=" mobile computing"> mobile computing</a> </p> <a href="https://publications.waset.org/abstracts/4077/ray-tracing-modified-3d-image-method-simulation-of-picocellular-propagation-channel-environment" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/4077.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">400</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">20035</span> Fracture Mechanics Modeling of a Shear-Cracked RC Beams Shear-Strengthened with FRP Sheets</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Shahriar%20Shahbazpanahi">Shahriar Shahbazpanahi</a>, <a href="https://publications.waset.org/abstracts/search?q=Alaleh%20Kamgar"> Alaleh Kamgar </a> </p> <p class="card-text"><strong>Abstract:</strong></p> So far, the conventional experimental and theoretical analysis in fracture mechanics have been applied to study concrete flexural- cracked beams, which are strengthened using fiber reinforced polymer (FRP) composite sheets. However, there is still little knowledge about the shear capacity of a side face FRP- strengthened shear-cracked beam. A numerical analysis is herein presented to model the fracture mechanics of a four-point RC beam, with two inclined initial notch on the supports, which is strengthened with side face FRP sheets. In the present study, the shear crack is forced to conduct by using an initial notch in supports. The ABAQUS software is used to model crack propagation by conventional cohesive elements. It is observed that the FRP sheets play important roles in preventing the propagation of shear cracks. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=crack" title="crack">crack</a>, <a href="https://publications.waset.org/abstracts/search?q=FRP" title=" FRP"> FRP</a>, <a href="https://publications.waset.org/abstracts/search?q=shear" title=" shear"> shear</a>, <a href="https://publications.waset.org/abstracts/search?q=strengthening" title=" strengthening"> strengthening</a> </p> <a href="https://publications.waset.org/abstracts/25999/fracture-mechanics-modeling-of-a-shear-cracked-rc-beams-shear-strengthened-with-frp-sheets" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/25999.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">550</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">20034</span> Electromagnetic Wave Propagation Equations in 2D by Finite Difference Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=N.%20Fusun%20Oyman%20Serteller">N. Fusun Oyman Serteller</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, the techniques to solve time dependent electromagnetic wave propagation equations based on the Finite Difference Method (FDM) are proposed by comparing the results with Finite Element Method (FEM) in 2D while discussing some special simulation examples. Here, 2D dynamical wave equations for lossy media, even with a constant source, are discussed for establishing symbolic manipulation of wave propagation problems. The main objective of this contribution is to introduce a comparative study of two suitable numerical methods and to show that both methods can be applied effectively and efficiently to all types of wave propagation problems, both linear and nonlinear cases, by using symbolic computation. However, the results show that the FDM is more appropriate for solving the nonlinear cases in the symbolic solution. Furthermore, some specific complex domain examples of the comparison of electromagnetic waves equations are considered. Calculations are performed through Mathematica software by making some useful contribution to the programme and leveraging symbolic evaluations of FEM and FDM. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=finite%20difference%20method" title="finite difference method">finite difference method</a>, <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=linear-nonlinear%20PDEs" title=" linear-nonlinear PDEs"> linear-nonlinear PDEs</a>, <a href="https://publications.waset.org/abstracts/search?q=symbolic%20computation" title=" symbolic computation"> symbolic computation</a>, <a href="https://publications.waset.org/abstracts/search?q=wave%20propagation%20equations" title=" wave propagation equations"> wave propagation equations</a> </p> <a href="https://publications.waset.org/abstracts/107982/electromagnetic-wave-propagation-equations-in-2d-by-finite-difference-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/107982.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">147</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">20033</span> Non-Linear Vibration and Stability Analysis of an Axially Moving Beam with Rotating-Prismatic Joint</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20Najafi">M. Najafi</a>, <a href="https://publications.waset.org/abstracts/search?q=F.%20Rahimi%20Dehgolan"> F. Rahimi Dehgolan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, the dynamic modeling of a single-link flexible beam with a tip mass is given by using Hamilton's principle. The link has been rotational and translational motion and it was assumed that the beam is moving with a harmonic velocity about a constant mean velocity. Non-linearity has been introduced by including the non-linear strain to the analysis. Dynamic model is obtained by Euler-Bernoulli beam assumption and modal expansion method. Also, the effects of rotary inertia, axial force, and associated boundary conditions of the dynamic model were analyzed. Since the complex boundary value problem cannot be solved analytically, the multiple scale method is utilized to obtain an approximate solution. Finally, the effects of several conditions on the differences among the behavior of the non-linear term, mean velocity on natural frequencies and the system stability are discussed. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=non-linear%20vibration" title="non-linear vibration">non-linear vibration</a>, <a href="https://publications.waset.org/abstracts/search?q=stability" title=" stability"> stability</a>, <a href="https://publications.waset.org/abstracts/search?q=axially%20moving%20beam" title=" axially moving beam"> axially moving beam</a>, <a href="https://publications.waset.org/abstracts/search?q=bifurcation" title=" bifurcation"> bifurcation</a>, <a href="https://publications.waset.org/abstracts/search?q=multiple%20scales%20method" title=" multiple scales method"> multiple scales method</a> </p> <a href="https://publications.waset.org/abstracts/67244/non-linear-vibration-and-stability-analysis-of-an-axially-moving-beam-with-rotating-prismatic-joint" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/67244.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">370</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">20032</span> Beam, Column Joints Concrete in Seismic Zone</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Khalifa%20Kherafa">Khalifa Kherafa</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This east project consists in studying beam–column joints concrete subjected to seismic loads. A bibliographical study was introduced to clarify the work undertaken by the researchers in the field during the three last decades and especially the two last year’s results which were to study for the determination of the method of calculating of transverse reinforcement in the various nodes of a structure. For application, the efforts in the posts el the beams of a building in R+4 in zone 3 were calculate according to the finite element method through the software <SAP 2000>. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=beam%E2%80%93column%20joints" title="beam–column joints">beam–column joints</a>, <a href="https://publications.waset.org/abstracts/search?q=cyclic%20loading" title=" cyclic loading"> cyclic loading</a>, <a href="https://publications.waset.org/abstracts/search?q=shearing%20force" title=" shearing force"> shearing force</a>, <a href="https://publications.waset.org/abstracts/search?q=damaged%20joint" title=" damaged joint"> damaged joint</a> </p> <a href="https://publications.waset.org/abstracts/23933/beam-column-joints-concrete-in-seismic-zone" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/23933.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">20031</span> Patented Free-Space Optical System for Auto Aligned Optical Beam Allowing to Compensate Mechanical Misalignments</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Aurelien%20Boutin">Aurelien Boutin</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In optical systems such as Variable Optical Delay Lines, where a collimated beam has to go back and forth, corner cubes are used in order to keep the reflected beam parallel to the incoming beam. However, the reflected beam can be laterally shifted, which will lead to losses. In this paper, we report on a patented optical design that allows keeping the reflected beam with the exact same position and direction whatever the displacement of the corner cube leading to zero losses. After explaining how the optical design works and theoretically allows to compensate for any defects in the translation of the corner cube, we will present the results of experimental comparisons between a standard layout (i.e., only corner cubes) and our optical layout. To compare both optical layouts, we used a fiber-to-fiber coupling setup. It consists of a couple of lights from one fiber to the other, thanks to two lenses. The ensemble [fiber+lense] is fixed and called a collimator so that the light is coupled from one collimator to another. Each collimator was precisely made in order to have a precise working distance. In the experiment, we measured and compared the Insertion Losses (IL) variations between both collimators with the distance between them (i.e., natural Gaussian beam coupling losses) and between both collimators in the different optical layouts tested, with the same optical length propagation. We will show that the IL variations of our setup are less than 0.05dB with respect to the IL variations of collimators alone. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=free-space%20optics" title="free-space optics">free-space optics</a>, <a href="https://publications.waset.org/abstracts/search?q=variable%20optical%20delay%20lines" title=" variable optical delay lines"> variable optical delay lines</a>, <a href="https://publications.waset.org/abstracts/search?q=optical%20cavity" title=" optical cavity"> optical cavity</a>, <a href="https://publications.waset.org/abstracts/search?q=auto-alignment" title=" auto-alignment"> auto-alignment</a> </p> <a href="https://publications.waset.org/abstracts/152717/patented-free-space-optical-system-for-auto-aligned-optical-beam-allowing-to-compensate-mechanical-misalignments" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/152717.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">20030</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">20029</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">20028</span> Structural Health Monitoring of Buildings–Recorded Data and Wave Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Tzong-Ying%20Hao">Tzong-Ying Hao</a>, <a href="https://publications.waset.org/abstracts/search?q=Mohammad%20T.%20Rahmani"> Mohammad T. Rahmani</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This article presents the structural health monitoring (SHM) method based on changes in wave traveling times (wave method) within a layered 1-D shear beam model of structure. The wave method measures the velocity of shear wave propagating in a building from the impulse response functions (IRF) obtained from recorded data at different locations inside the building. If structural damage occurs in a structure, the velocity of wave propagation through it changes. The wave method analysis is performed on the responses of Torre Central building, a 9-story shear wall structure located in Santiago, Chile. Because events of different intensity (ambient vibrations, weak and strong earthquake motions) have been recorded at this building, therefore it can serve as a full-scale benchmark to validate the structural health monitoring method utilized. The analysis of inter-story drifts and the Fourier spectra for the EW and NS motions during 2010 Chile earthquake are presented. The results for the NS motions suggest the coupling of translation and torsion responses. The system frequencies (estimated from the relative displacement response of the 8th-floor with respect to the basement from recorded data) were detected initially decreasing approximately 24% in the EW motion. Near the end of shaking, an increase of about 17% was detected. These analysis and results serve as baseline indicators of the occurrence of structural damage. The detected changes in wave velocities of the shear beam model are consistent with the observed damage. However, the 1-D shear beam model is not sufficient to simulate the coupling of translation and torsion responses in the NS motion. The wave method is proven for actual implementation in structural health monitoring systems based on carefully assessing the resolution and accuracy of the model for its effectiveness on post-earthquake damage detection in buildings. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Chile%20earthquake" title="Chile earthquake">Chile earthquake</a>, <a href="https://publications.waset.org/abstracts/search?q=damage%20detection" title=" damage detection"> damage detection</a>, <a href="https://publications.waset.org/abstracts/search?q=earthquake%20response" title=" earthquake response"> earthquake response</a>, <a href="https://publications.waset.org/abstracts/search?q=impulse%20response%20function" title=" impulse response function"> impulse response function</a>, <a href="https://publications.waset.org/abstracts/search?q=shear%20beam%20model" title=" shear beam model"> shear beam model</a>, <a href="https://publications.waset.org/abstracts/search?q=shear%20wave%20velocity" title=" shear wave velocity"> shear wave velocity</a>, <a href="https://publications.waset.org/abstracts/search?q=structural%20health%20monitoring" title=" structural health monitoring"> structural health monitoring</a>, <a href="https://publications.waset.org/abstracts/search?q=torre%20central%20building" title=" torre central building"> torre central building</a>, <a href="https://publications.waset.org/abstracts/search?q=wave%20method" title=" wave method"> wave method</a> </p> <a href="https://publications.waset.org/abstracts/27731/structural-health-monitoring-of-buildings-recorded-data-and-wave-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/27731.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">367</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">20027</span> Modified Side Plate Design to Suppress Lateral Torsional Buckling of H-Beam for Seismic Application</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Erwin">Erwin</a>, <a href="https://publications.waset.org/abstracts/search?q=Cheng-Cheng%20Chen"> Cheng-Cheng Chen</a>, <a href="https://publications.waset.org/abstracts/search?q=Charles%20J.%20Salim"> Charles J. Salim</a> </p> <p class="card-text"><strong>Abstract:</strong></p> One of the method to solve the lateral torsional buckling (LTB) problem is by using side plates to increased the buckling resistance of the beam. Some modifications in designing the side plates are made in this study to simplify the construction in the field and reduce the cost. At certain region, side plates are not added: (1) At the beam end to preserve some spaces for bolt installation, but the beam is strengthened by adding cover plate at both flanges and (2) at the middle span of the beam where the moment is smaller. Three small scale full span beam specimens are tested under cyclic loading to investigate the LTB resistant and the ductility of the proposed design method. Test results show that the LTB deformation can be effectively suppressed and very high ductility level can be achieved. Following the test, a finite element analysis (FEA) model is established and is verified using the test results. An intensive parametric study is conducted using the established FEA model. The analysis reveals that the length of side plates is the most important parameter determining the performance of the beam and the required side plates length is determined by some parameters which are (1) beam depth to flange width ratio, (2) beam slenderness ratio (3) strength and thickness of the side plates, (4) compactness of beam web and flange, and (5) beam yield strength. At the end of the paper, a design formula to calculate the required side plate length is suggested. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=cover%20plate" title="cover plate">cover plate</a>, <a href="https://publications.waset.org/abstracts/search?q=earthquake%20resistant%20design" title=" earthquake resistant design"> earthquake resistant design</a>, <a href="https://publications.waset.org/abstracts/search?q=lateral%20torsional%20buckling" title=" lateral torsional buckling"> lateral torsional buckling</a>, <a href="https://publications.waset.org/abstracts/search?q=side%20plate" title=" side plate"> side plate</a>, <a href="https://publications.waset.org/abstracts/search?q=steel%20structure" title=" steel structure"> steel structure</a> </p> <a href="https://publications.waset.org/abstracts/96206/modified-side-plate-design-to-suppress-lateral-torsional-buckling-of-h-beam-for-seismic-application" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/96206.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">175</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">20026</span> Minimization of Propagation Delay in Multi Unmanned Aerial Vehicle Network</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Purva%20Joshi">Purva Joshi</a>, <a href="https://publications.waset.org/abstracts/search?q=Rohit%20Thanki"> Rohit Thanki</a>, <a href="https://publications.waset.org/abstracts/search?q=Omar%20Hanif"> Omar Hanif</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Unmanned aerial vehicles (UAVs) are becoming increasingly important in various industrial applications and sectors. Nowadays, a multi UAV network is used for specific types of communication (e.g., military) and monitoring purposes. Therefore, it is critical to reducing propagation delay during communication between UAVs, which is essential in a multi UAV network. This paper presents how the propagation delay between the base station (BS) and the UAVs is reduced using a searching algorithm. Furthermore, the iterative-based K-nearest neighbor (k-NN) algorithm and Travelling Salesmen Problem (TSP) algorthm were utilized to optimize the distance between BS and individual UAV to overcome the problem of propagation delay in multi UAV networks. The simulation results show that this proposed method reduced complexity, improved reliability, and reduced propagation delay in multi UAV networks. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=multi%20UAV%20network" title="multi UAV network">multi UAV network</a>, <a href="https://publications.waset.org/abstracts/search?q=optimal%20distance" title=" optimal distance"> optimal distance</a>, <a href="https://publications.waset.org/abstracts/search?q=propagation%20delay" title=" propagation delay"> propagation delay</a>, <a href="https://publications.waset.org/abstracts/search?q=K%20-%20nearest%20neighbor" title=" K - nearest neighbor"> K - nearest neighbor</a>, <a href="https://publications.waset.org/abstracts/search?q=traveling%20salesmen%20problem" title=" traveling salesmen problem"> traveling salesmen problem</a> </p> <a href="https://publications.waset.org/abstracts/150423/minimization-of-propagation-delay-in-multi-unmanned-aerial-vehicle-network" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/150423.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">200</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">20025</span> Nonlinear Finite Element Modeling of Deep Beam Resting on Linear and Nonlinear 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> An accuracy nonlinear analysis of a deep beam resting on elastic perfectly plastic soil is carried out in this study. In fact, a nonlinear finite element modeling for large deflection and moderate rotation of Euler-Bernoulli beam resting on linear and nonlinear random soil is investigated. The geometric nonlinear analysis of the beam is based on the theory of von Kàrmàn, where the Newton-Raphson incremental iteration method is implemented in a Matlab code to solve the nonlinear equation of the soil-beam interaction system. However, two analyses (deterministic and probabilistic) are proposed to verify the accuracy and the efficiency of the proposed model where the theory of the local average based on the Monte Carlo approach is used to analyze the effect of the spatial variability of the soil properties on the nonlinear beam response. The effect of six main parameters are investigated: the external load, the length of a beam, the coefficient of subgrade reaction of the soil, the Young’s modulus of the beam, the coefficient of variation and the correlation length of the soil’s coefficient of subgrade reaction. A comparison between the beam resting on linear and nonlinear soil models is presented for different beam’s length and external load. Numerical results have been obtained for the combination of the geometric nonlinearity of beam and material nonlinearity of random soil. This comparison highlighted the need of including the material nonlinearity and spatial variability of the soil in the geometric nonlinear analysis, when the beam undergoes large deflections. <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=geometric%20nonlinearity" title=" geometric nonlinearity"> geometric nonlinearity</a>, <a href="https://publications.waset.org/abstracts/search?q=material%20nonlinearity" title=" material nonlinearity"> material nonlinearity</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=spatial%20variability" title=" spatial variability"> spatial variability</a> </p> <a href="https://publications.waset.org/abstracts/40934/nonlinear-finite-element-modeling-of-deep-beam-resting-on-linear-and-nonlinear-random-soil" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/40934.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">414</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">20024</span> Simulations of High-Intensity, Thermionic Electron Guns for Electron Beam Thermal Processing Including Effects of Space Charge Compensation </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=O.%20Hinrichs">O. Hinrichs</a>, <a href="https://publications.waset.org/abstracts/search?q=H.%20Franz"> H. Franz</a>, <a href="https://publications.waset.org/abstracts/search?q=G.%20Reiter"> G. Reiter</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Electron guns have a key function in a series of thermal processes, like EB (electron beam) melting, evaporation or welding. These techniques need a high-intensity continuous electron beam that defocuses itself due to high space charge forces. A proper beam transport throughout the magnetic focusing system can be ensured by a space charge compensation via residual gas ions. The different pressure stages in the EB gun cause various degrees of compensation. A numerical model was installed to simulate realistic charge distributions within the beam by using CST-Particle Studio code. We will present current status of beam dynamic simulations. This contribution will focus on the creation of space charge ions and their influence on beam and gun components. Furthermore, the beam transport in the gun will be shown for different beam parameters. The electron source allows to produce beams with currents of 3 A to 15 A and energies of 40 keV to 45 keV. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=beam%20dynamic%20simulation" title="beam dynamic simulation">beam dynamic simulation</a>, <a href="https://publications.waset.org/abstracts/search?q=space%20charge%20compensation" title=" space charge compensation"> space charge compensation</a>, <a href="https://publications.waset.org/abstracts/search?q=thermionic%20electron%20source" title=" thermionic electron source"> thermionic electron source</a>, <a href="https://publications.waset.org/abstracts/search?q=EB%20melting" title=" EB melting"> EB melting</a>, <a href="https://publications.waset.org/abstracts/search?q=EB%20thermal%20processing" title=" EB thermal processing "> EB thermal processing </a> </p> <a href="https://publications.waset.org/abstracts/106185/simulations-of-high-intensity-thermionic-electron-guns-for-electron-beam-thermal-processing-including-effects-of-space-charge-compensation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/106185.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">336</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">20023</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">20022</span> Relating Interface Properties with Crack Propagation in Composite Laminates </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Tao%20Qu">Tao Qu</a>, <a href="https://publications.waset.org/abstracts/search?q=Chandra%20Prakash"> Chandra Prakash</a>, <a href="https://publications.waset.org/abstracts/search?q=Vikas%20Tomar"> Vikas Tomar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The interfaces between organic and inorganic phases in natural materials have been shown to be a key factor contributing to their high performance. This work analyzes crack propagation in a 2-ply laminate subjected to uniaxial tensile mode-I crack propagation loading that has laminate properties derived based on biological material constituents (marine exoskeleton- chitin and calcite). Interfaces in such laminates are explicitly modeled based on earlier molecular simulations performed by authors. Extended finite element method and cohesive zone modeling based simulations coupled with theoretical analysis are used to analyze crack propagation. Analyses explicitly quantify the effect that interface mechanical property variation has on the delamination as well as the transverse crack propagation in examined 2-ply laminates. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=chitin" title="chitin">chitin</a>, <a href="https://publications.waset.org/abstracts/search?q=composites" title=" composites"> composites</a>, <a href="https://publications.waset.org/abstracts/search?q=interfaces" title=" interfaces"> interfaces</a>, <a href="https://publications.waset.org/abstracts/search?q=fracture" title=" fracture"> fracture</a> </p> <a href="https://publications.waset.org/abstracts/44635/relating-interface-properties-with-crack-propagation-in-composite-laminates" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/44635.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">382</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">20021</span> On the Evaluation of Critical Lateral-Torsional Buckling Loads of Monosymmetric Beam-Columns</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=T.%20Yilmaz">T. Yilmaz</a>, <a href="https://publications.waset.org/abstracts/search?q=N.%20Kirac"> N. Kirac</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Beam-column elements are defined as structural members subjected to a combination of axial and bending forces. Lateral torsional buckling is one of the major failure modes in which beam-columns that are bent about its strong axis may buckle out of the plane by deflecting laterally and twisting. This study presents a compact closed-form equation that it can be used for calculating critical lateral torsional-buckling load of beam-columns with monosymmetric sections in the presence of a known axial load. Lateral-torsional buckling behavior of beam-columns subjected to constant axial force and various transverse load cases are investigated by using Ritz method in order to establish proposed equation. Lateral-torsional buckling loads calculated by presented formula are compared to finite element model results. ABAQUS software is utilized to generate finite element models of beam-columns. It is found out that lateral-torsional buckling load of beam-columns with monosymmetric sections can be determined by proposed equation and can be safely used in design. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=lateral-torsional%20buckling" title="lateral-torsional buckling">lateral-torsional buckling</a>, <a href="https://publications.waset.org/abstracts/search?q=stability" title=" stability"> stability</a>, <a href="https://publications.waset.org/abstracts/search?q=beam-column" title=" beam-column"> beam-column</a>, <a href="https://publications.waset.org/abstracts/search?q=monosymmetric%20section" title=" monosymmetric section"> monosymmetric section</a> </p> <a href="https://publications.waset.org/abstracts/51595/on-the-evaluation-of-critical-lateral-torsional-buckling-loads-of-monosymmetric-beam-columns" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/51595.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">324</span> </span> </div> </div> <ul class="pagination"> <li class="page-item disabled"><span class="page-link">‹</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=finite-difference%20beam%20propagation%20method&page=2">2</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=finite-difference%20beam%20propagation%20method&page=3">3</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=finite-difference%20beam%20propagation%20method&page=4">4</a></li> <li class="page-item"><a class="page-link" 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