Analytical solutions for in-plane dominated vibrations of transversely isotropic circular plates based on high-order theories

Abstract

In this paper, three high-order shear deformation theories are presented to investigate in-plane dominated vibrations for circular transversely isotropic plates. The equations of motion for the in-plane dominated vibrations of circular plates based on high-order theories are first derived using Hamilton's principle. Natural frequencies and corresponding mode shapes are determined by solving the equations of motion and boundary conditions. Comparisons of resonant frequencies and associated mode shapes arising from the first-order shear deformation plate theory (FSDT), second-order shear deformation plate theory (SSDT), third-order shear deformation plate theory (TSDT), and the three-dimensional finite element method (FEM) are used for fully free and clamped circular plates. It is shown that the results obtained by the three analytical solutions and numerical calculations for the natural frequencies and corresponding mode shapes are in excellent agreement.