An extended separation-of-variable method for free vibrations of orthotropic rectangular thin plate assemblies

摘要

Rectangular plate assemblies are widely used in various engineering fields, but there are not closed-form solutions for them with arbitrary homogeneous boundary conditions. Hence, this work is to develop an extended separation-of-variable method to achieve closed-form analytical solutions for the vibrating problems of orthotropic rectangular thin plate assemblies. In this method, the mode function of each plate is in an explicit separation-of-variable form, and the frequencies corresponding to two-direction eigenfunctions are mathematically independent of each other. This method can deal with all homogeneous boundary conditions. The two-direction eigenvalue equations can be solved simultaneously, and the obtained closed-form eigensolutions satisfy the Rayleigh's principle exactly. Numerical experiments validate the accuracy of the present solutions, and parametric study is conducted.