中文摘要：

研究了正交各向异性功能梯度平板的二维热弹性振动问题．该平板在Y方向无限长，z方向对边简支且温度恒定．从热弹性力学的基本方程出发，假设材料参数沿板厚方向（z方向）按任意函数规律变化，基于状态空间法，在板的上下表面作用机械荷载和热荷载的情况下，获得了功能梯度平板二维热弹性振动问题的Peano-Baker级数解．通过算例，验证了Peano-Baker级数解的正确性，同时也分析了材料参数沿板厚方向为线性分布时不同的激励频率对平板响应的影响．结果表明：位移、应力均随着激励频率接近板的固有频率时，其值也增大．

英文摘要：

Two-dimensional thermoelasticity vibration was analyzed for an orthotropic functionally graded plate with infinite length along y-direction and simple support and constant temperature at two opposite edges in x-direction. According to the basic equations of thermoelasticity, assuming that the material had arbitrary variation property along plate-thickness direction（z-direction） , Peano-Baker series solution was obtained for the thermoelasticity vibration problem of the functionally graded plate with mechanical and thermal loads on upper and lower surfaces by state-space method. The series solution was verified through numerical examples. The influence of forced frequency on structural response of the plate was also inves- tigated with material properties of linear dependence on thickness-coordinate. The results show that physi- cal quantities of displacements and stresses are increased with the increasing of forced frequency near to the inherent frequency.