Free vibration of orthotropic Levy-type solution plates by using SEM

Abstract

Orthotropic Levy-type solution plates considering shear deformation were solved by using the Spectral Element Method (SEM). In SEM, the exact solution of structural dynamic related problems can be solved by using the frequency-dependent shape functions. The solutions of SEM are accurate in decreasing the amount of Degree Of Freedoms (DOF) to discard the cost and computational disadvantages in the Finite Element Method (FEM). This study investigates the free vibration problems of orthotropic Levy-type solution plates solutions based on the two variable Refined Plate Theory (RPT). SEM for orthotropic Levy-type solution plates in the frequency domain was formulated to solve free vibration problems. The differential governing equations of the orthotropic plate element in SEM are formulated into the form of transcendental stiffness matrices. The boundary conditions of the spectral element model consist of four edge-type DOFs at each side of the orthotropic Levy-type solution plates. The natural frequencies of the plate are calculated by means of the Wittrick-Williams procedure. The numerical investigations are presented to show the accuracy, efficiency, and effectiveness of SEM without any discretization scheme.