Free and Forced Transverse Vibration Analysis of Moderately Thick Orthotropic Plates Using Spectral Finite Element Method

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.