Based on modified strain gradient theory, nonlinear vibration analysis of a functionally graded piezoelectric doubly curved microshell in thermal environment has been performed in this research. Three scale parameters have been included in the modeling of thin doubly curved microshell in order to capture micro-size effects. Graded material properties between the top and bottom surfaces of functionally graded piezoelectric doubly curved microshell have been considered via incorporating power-law model. It is also assumed that the microshell is exposed to a temperature field of uniform type and the material properties are temperature-dependent. By analytically solving the governing equations based on the harmonic balance method, the closed form of nonlinear vibration frequency has been achieved. Obtained results indicate the relevance of calculated frequencies to three scale parameters, material gradation, electrical voltage, curvature radius, and temperature changes.

本研究基于修正应变梯度理论，对热环境下功能梯度压电双曲面微壳进行了非线性振动分析。三个尺度参数已包含在薄双弯曲微壳的建模中，以捕捉微尺寸效应。已经通过结合幂律模型考虑了功能梯度压电双弯曲微壳的顶面和底面之间的梯度材料特性。还假设微壳暴露在均匀类型的温度场中，并且材料特性与温度有关。基于谐波平衡法对控制方程进行解析求解，得到非线性振动频率的闭合形式。