Solutions to nonlinear free vibration analysis of an arbitrarily laminated thin rectangular plate subjected to thermo-piezoelectric load is investigated. The governing equation of motion is based on von Kármán’s deflection of thin plates to capture the effects of moderate geometric nonlinearity. Induced strain actuation assumption is confined to a linear model for applied low electric fields and varying temperature distribution along the thickness direction. The solution for lateral displacement field for simply supported and clamped condition edges are determined by displacement-stress; mixed formulation. The applied Galerkin’s projection reduces the governing nonlinear partial differential equation to a time dependent ordinary differential equation. Solutions are obtained using a predictor-corrector numerical integration scheme. The effects of random applied actuation potential and thermal loading on nonlinear frequency ratio is examined. The marginal values provided using various probabilistic methods are found to be in good agreement with each other.

研究了任意叠层矩形矩形薄板在热压电作用下的非线性自由振动分析方法。运动的控制方程基于冯·卡尔曼薄板的挠度，以捕获中等几何非线性的影响。感应应变驱动假设仅限于线性模型，用于施加的低电场和沿厚度方向变化的温度分布。对于简单支撑和夹紧的状态边，横向位移场的解是由位移应力确定的。混合配方。应用的Galerkin投影将控制非线性偏微分方程简化为与时间相关的常微分方程。使用预测器-校正器数值积分方案获得解。研究了随机施加的驱动电位和热负荷对非线性频率比的影响。发现使用各种概率方法提供的边际值彼此非常一致。