Free vibration of a Levy-type solution for plates based on two-variable refined plate theory by using SEM

Abstract

The exact solution of structural dynamic related problems can be achieved by using the frequency-dependent spectral method. The exact solution is thought to be accurate while reducing the number of degree-of-freedom to resolve the cost and computational drawbacks. This paper investigates the vibrational characteristics of a Levy-type solution of thick plates considering shear deformation based on the two-variable Refined Plate Theory (RPT). The plates, which are modeled by an isotropic Levy-type rectangular plate, were solved by using the Spectral Element Method (SEM). The SEM for RPT Levy-type in the frequency domain is derived to formulate the free vibration problems of the plates. Transcendental stiffness matrices are well established in vibration, formulated from the exact solutions of the differential equations of the RPT Levy-type plate element. The present spectral element model has four line-type degree-of-freedoms (DOF) on each edge of the Levy-type rectangular plate. Natural frequencies of the plate are computed by means of the Wittrick-Williams algorithm. Numerical comparisons are given to show the effectiveness, efficiency, and accuracy of the SEM by using one element. Unlike the FEM, the SEM gives exact solutions of the natural frequencies of plates without element discretization procedures.

A general electroelastic analysis of piezoelectric shells based on levy-type solution and eigenvalue-eigenvector method

“…The governing equations of motion were solved using Fourier series and Galerkin's technique to investigate impact of geometrical parameters and applied voltage on the nonlinear responses. Kiryu et al [ 21 ] employed two variable plate theory for free vibration investigation of a plate based on Levy type method for specific boundary conditions. The responses were obtained using the frequency dependent spectral scheme.…”