In this paper, nonlinear vibrational behaviors of doubly-curved functionally graded piezoelectric (FGP) microshells in thermal environments have been studied. The doubly-curved microshell has been modeled by using modified couple stress and thin shell theories. The microshell has two material constituents which are piezoelectric materials and their gradation is described using power-law functions. Temperature fields are considered to be uniform, linear, and nonlinear. A closed-form of nonlinear vibration frequency has been obtained by analytically solving the governing equations using the Harmonic balance method. It will be demonstrated that nonlinear vibrational frequency of doubly-curved microshell relies on couple stress influence, material gradation, curvature radius, center deflection, and electrical field.

在本文中，研究了双曲线功能梯度压电 (FGP) 微壳在热环境中的非线性振动行为。双弯曲微壳已通过使用修正的耦合应力和薄壳理论建模。微壳具有两种材料成分，即压电材料，并且使用幂律函数描述它们的等级。温度场被认为是均匀的、线性的和非线性的。通过使用谐波平衡方法对控制方程进行解析求解，获得了非线性振动频率的闭合形式。将证明双曲面微壳的非线性振动频率依赖于耦合应力影响、材料级配、曲率半径、中心偏转和电场。