Modeling wave propagation in moderately thick rectangular plates using the spectral element method

Abstract

This paper presents development of the spectral element method (SEM) to specify natural frequencies and dynamic response of moderately thick rectangular plates under impact and moving loads. To solve differential equations of moderately thick plate, the displacement field has been expressed in the frequency domain using Fast Fourier Transformation (FFT) algorithm while considering simple boundary conditions for two parallel edges. Closed-form solutions have been derived for the differential equations in frequency domain. Deriving exact shape functions of plate in frequency domain, the dynamic solution in time domain has been calculated using Inverse Fast Fourier Transformation (IFFT). In this study, natural frequencies for moderately thick plates with variable and constant thicknesses have been calculated and compared to the past research results. Mode shapes of plates with various boundary conditions have been plotted. Moreover, plate’s displacements under impact and moving loads have been calculated using developed SEM. The utilization of a minimum numbers of elements in SEM, consequently leading to a considerable decrease in computational costs, is the main advantage of this method.