فهرس المقالات Spectral finite element method

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  1 - Spectral Finite Element Method for Free Vibration of Axially Moving Plates Based on First-Order Shear Deformation Theory
  M.R Bahrami S Hatami
  In this paper, the free vibration analysis of moderately thick rectangular plates axially moving with constant velocity and subjected to uniform in-plane loads is investigated by the spectral finite element method. Two parallel edges of the plate are assumed to be simpl أکثر

  In this paper, the free vibration analysis of moderately thick rectangular plates axially moving with constant velocity and subjected to uniform in-plane loads is investigated by the spectral finite element method. Two parallel edges of the plate are assumed to be simply supported and the remaining edges have any arbitrary boundary conditions. Using Hamilton’s principle, three equations of motion for the plate are developed based on first-order shear deformation theory. The equations are transformed from the time domain into the frequency domain by assuming harmonic solutions. Then, the frequency-dependent dynamic shape functions obtained from the exact solution of the governing differential equations is used to develop the spectral stiffness matrix. By solving a non-standard eigenvalue problem, the natural frequencies and the critical speeds of the moving plates are obtained. The exactness and validity of the results are verified by comparing them with the results in previous studies. By the developed method some examples for vibration of stationary and moving moderately thick plates with different boundary conditions are presented. The effects of some parameters such as the axially speed of plate motion, the in-plane forces, aspect ratio and length to thickness ratio on the natural frequencies and the critical speeds of the moving plate are investigated. These results can be used as a benchmark for comparing the accuracy and precision of the other analytical and numerical methods. تفاصيل المقالة
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  2 - Free and Forced Transverse Vibration Analysis of Moderately Thick Orthotropic Plates Using Spectral Finite Element Method
  M.R Bahrami S Hatami
  In the present study, a spectral finite element method is developed for free and forced transverse vibration of Levy-type moderately thick rectangular orthotropic plates based on first-order shear deformation theory. Levy solution assumption was used to convert the two- أکثر

  In the present study, a spectral finite element method is developed for free and forced transverse vibration of Levy-type moderately thick rectangular orthotropic plates based on first-order shear deformation theory. Levy solution assumption was used to convert the two-dimensional problem into a one-dimensional problem. In the first step, the governing out-of-plane differential equations are transformed from time domain into frequency domain by discrete Fourier transform theory. Then, the spectral stiffness matrix is formulated, using frequency-dependent dynamic shape functions which are obtained from the exact solution of the governing differential equations. An efficient numerical algorithm, using drawing method is used to extract the natural frequencies. The frequency domain dynamic responses are obtained from solution of the spectral element equation. Also, the time domain dynamic responses are derived by using inverse discrete Fourier transform algorithm. The accuracy and excellent performance of the spectral finite element method is then compared with the results obtained from closed form solution methods in previous studies. Finally, comprehensive results for out-of-plane natural frequencies and transverse displacement of the moderately thick rectangular plates with six different combinations of boundary conditions are presented. These results can serve as a benchmark to compare the accuracy and precision of the numerical methods used. تفاصيل المقالة