A coupled thermomechanics approach for frequency information of electrically composite microshell using heat-transfer co
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A coupled thermomechanics approach for frequency information of electrically composite microshell using heat-transfer continuum problem M. S. H. Al-Furjan1,2,a , Mostafa Habibi3,4,b , Farzad Ebrahimi5,c , Guojin Chen1,d , Mehran Safarpour6,e , Hamed Safarpour5,f 1 School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou 310018, China 2 School of Materials Science and Engineering, State Key Laboratory of Silicon Materials, Zhejiang
University, Hangzhou 310027, China
3 Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam 4 Faculty of Electrical–Electronic Engineering, Duy Tan University, Da Nang 550000, 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
Received: 5 June 2020 / Accepted: 7 September 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 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
a e-mail: [email protected] b e-mail: [email protected] (corresponding author) c e-mail: [email protected] (corresponding author) d e-mail: [email protected] e e-mail: [email protected] f e-mail: [email protected]
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Eur. Phys. J. Plus
(2020) 135:837
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