The objective of this paper is to provide a computational method to analyze free vibrations of advanced composite plates in thermal environments according to a recently developed higher-order shear deformation theory. This method is based upon the assumptions that displacements field include just four unknowns and considers a combination of trigonometric and exponential shear shape functions which satisfy shear stress free boundary conditions on the plate surfaces. The FG plates are simply supported and subjected to uniform, linear, nonlinear and sinusoidal temperature rise. The temperature field considered is assumed to vary in the thickness direction and constant in the axial directions of plates. It is supposed that the constituent materials possess temperature-dependent properties changing across the thickness with a simple power law function. The equations of motion are obtained by employing Hamilton’s principle and solved based on Navier’s method to determine natural frequencies of the FG plate. A parametric study for FGM plates with different values of power law index and under different sets of thermal environmental conditions has been carried out. The obtained results are compared for temperature-dependent and temperature-independent FG Plates and validated with available results in the literature.

本文的目的是根据最近发展的高阶剪切变形理论，提供一种计算方法来分析高级复合板在热环境中的自由振动。该方法基于以下假设：位移场仅包括四个未知数，并考虑了三角和指数剪切形状函数的组合，这些函数满足了板表面上无剪切应力的边界条件。简单地支撑FG板并使其均匀，线性，非线性和正弦形的温度上升。假定所考虑的温度场在厚度方向上变化并且在板的轴向方向上恒定。假定组成材料具有随温度变化的特性，该特性随厚度随简单的幂律函数而变化。通过采用汉密尔顿原理获得运动方程，并根据纳维耶方法求解运动方程，以确定FG板的固有频率。对具有不同幂律指数值和在不同热环境条件下的FGM板进行了参数研究。将获得的结果与温度相关的FG板和温度无关的FG板进行比较，并用文献中的可用结果进行验证。