Eur. Phys. J. Plus (2020) 135: 837
https://doi.org/10.1140/epjp/s13360-020-00764-3

Regular Article

A coupled thermomechanics approach for frequency information of electrically composite microshell using heat-transfer continuum problem

¹ School of Mechanical Engineering, Hangzhou Dianzi University, 310018, Hangzhou, China
² School of Materials Science and Engineering, State Key Laboratory of Silicon Materials, Zhejiang University, 310027, Hangzhou, China
³ Institute of Research and Development, Duy Tan University, 550000, Da Nang, Vietnam
⁴ Faculty of Electrical–Electronic Engineering, Duy Tan University, 550000, Da Nang, Vietnam
⁵ Faculty of Engineering, Department of Mechanics, Imam Khomeini International University, Qazvin, Iran
⁶ Department of Mechanical Engineering, Faculty of Engineering, Tarbiat Modares University, Tehran, Iran

^b mostafahabibi@duytan.edu.vn
^c febrahimy@gmail.com

Received: 5 June 2020
Accepted: 7 September 2020
Published online: 16 October 2020

Abstract

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.