Vibrations of a plate with periodically changing parameters (Q2668907)

In this paper, the equation of vibrations of a plate with periodically changing parameters (material properties and thickness) are derived, and the eigenfrequencies are determined. Solution of the problem is obtained with the approximate theory (Bubnov-Galerkin method). The approximate results are presented by analytical formulas. Asymptotic averaging (implemented in Wolfram Mathematica) and the finite element software ANSYS are used to determine the eigenfrequencies. Numerical and asymptotic results are compared. Fixed boundaries of the plate and hinged support boundaries are considered. A comparison of the analytical results and the numerical results obtained by the finite element method using the ANSYS software package is presented. The relative error of the calculations is shown to be no larger than 3\%. The materials considered are steel and titanium.