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.

本文提出了三种高阶剪切变形理论来研究圆形横向各向同性板的面内支配振动。首先基于汉密尔顿原理，推导了基于高阶理论的圆盘面内支配振动的运动方程。通过求解运动方程和边界条件，可以确定固有频率和相应的振型。一阶剪切变形板理论（FSDT），二阶剪切变形板理论（SSDT），三阶剪切变形板理论（TSDT）和三维有限元产生的共振频率和相关模式形状的比较单元法（FEM）用于完全自由和夹紧的圆板。