Damped vibration of a graphene sheet using a higher-order nonlocal strain-gradient Kirchhoff plate model

Davood Shahsavari; Behrouz Karami; Li Li

doi:10.1016/j.crme.2018.08.011

Damped vibration of a graphene sheet using a higher-order nonlocal strain-gradient Kirchhoff plate model

Davood Shahsavari ¹; Behrouz Karami ¹ ; Li Li ²

¹ Department of Mechanical Engineering, Marvdasht Branch, Islamic Azad University, Marvdasht, Iran
² State Key Lab of Digital Manufacturing Equipment and Technology, School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China

Comptes Rendus. Mécanique, Volume 346 (2018) no. 12, pp. 1216-1232.

Abstract

A higher-order nonlocal strain-gradient model is presented for the damped vibration analysis of single-layer graphene sheets (SLGSs) in hygrothermal environment. Based on Kirchhoff plate theory in conjunction with a higher-order (bi-Helmholtz) nonlocal strain gradient theory, the equations of motion are obtained using Hamilton's principle. The higher-order nonlocal strain gradient theory has lower- and higher-order nonlocal parameters and a material characteristic parameter. The presented model can reasonably interpret the softening effects of the SLGS, and indicates a reasonably good match with the experimental flexural frequencies. Finally, the roles of viscous and structural damping coefficients, small-scale parameters, hygrothermal environment and elastic foundation on the vibrational responses of SLGSs are studied in detail.

Received: 2018-05-22
Accepted: 2018-08-24
Published online: 2018-09-05

DOI: 10.1016/j.crme.2018.08.011

Keywords: Damped vibration, Bi-Helmholtz nonlocal strain gradient theory, Environmental effects, Graphene, Visco-Pasternak foundation

Author's affiliations:

Davood Shahsavari ¹; Behrouz Karami ¹; Li Li ²

¹ Department of Mechanical Engineering, Marvdasht Branch, Islamic Azad University, Marvdasht, Iran
² State Key Lab of Digital Manufacturing Equipment and Technology, School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China

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     author = {Davood Shahsavari and Behrouz Karami and Li Li},
     title = {Damped vibration of a graphene sheet using a higher-order nonlocal strain-gradient {Kirchhoff} plate model},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {1216--1232},
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Davood Shahsavari; Behrouz Karami; Li Li. Damped vibration of a graphene sheet using a higher-order nonlocal strain-gradient Kirchhoff plate model. Comptes Rendus. Mécanique, Volume 346 (2018) no. 12, pp. 1216-1232. doi : 10.1016/j.crme.2018.08.011. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2018.08.011/

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