This article analyzes critical voltage and frequency information of functionally graded graphene nanoplatelets-reinforced composite (FG-GPLRC) porous cylindrical microshell embedded in piezoelectric layer, subjected to temperature gradient. The current non-classical model is capable of capturing the size dependency in the microshells by using only one material length scale parameter; moreover, the mathematical formulation of microshells based on the classical model can be recovered from the present model by neglecting the material length scale parameter. To satisfy temperature boundary conditions, the Fourier series solution is extracted. In addition, for the first time, thermal conductivity coefficients regarding each GPL’s distribution pattern are presented. The thermally equations are solved via Heun’s differential equation. The mechanical properties of FG-GPLRC layer are estimated based on modified Halpin–Tsai micromechanics and rule of mixtures. Hamilton’s principle is utilized to develop governing equations of motion and boundary conditions. Finally, an analytical solution is carried out based on Navier method to obtain critical voltage and frequency in the case of simply supported shell, whereas a semi-analytical solution is proposed based on differential quadrature method (DQM) for other boundary conditions. The results show that piezoelectric layer, graphene nanoplatelets’ (GPLs) distribution pattern, porosity distribution, difference gradient thermal, length scale parameter and GPL weight function play important roles on the natural frequency and critical voltage of the GPL porous cylindrical microshell coupled with piezoelectric actuator. The results of the current study are useful suggestions for the design of materials science, micro-electromechanical systems and nano-electromechanical systems such as nano-actuators and nano-sensors.

本文分析了温度梯度下功能梯度石墨烯纳米片增强复合材料（FG-GPLRC）多孔圆柱微壳嵌入压电层的临界电压和频率信息。当前的非经典模型能够通过仅使用一个材料长度比例参数来捕获微壳中的尺寸依赖性。此外，通过忽略材料长度尺度参数，可以从当前模型中恢复基于经典模型的微壳的数学公式。为了满足温度边界条件，提取了傅里叶级数解。此外，首次提出了有关每个GPL分布模式的导热系数。通过Heun微分方程求解热方程。FG-GPLRC层的机械性能是基于改进的Halpin-Tsai微力学和混合物规则估算的。汉密尔顿原理被用来发展运动和边界条件的控制方程。最后，基于Navier方法进行了解析求解，以得到简单支撑壳的临界电压和频率，而针对其他边界条件，提出了基于差分正交方法（DQM）的半解析解。结果表明，压电层，石墨烯纳米片（GPLs）的分布模式，孔隙率分布，差梯度热，长度尺度参数和GPL重量函数对耦合压电致动器的GPL多孔圆柱微壳的固有频率和临界电压起重要作用。 。