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ARTICLE
A simplified elliptical function solution for coupled nonlinear vibration of multilayer graphene sheets
| 1 | PSG College of Technology, Department of Civil Engineering, Coimbatore, India |
CORRESPONDING AUTHOR
G. Venkatraman
Department of Civil Engineering, PSG College of Technology, 641004, Coimbatore, India
Department of Civil Engineering, PSG College of Technology, 641004, Coimbatore, India
Submission date: 2021-06-17
Final revision date: 2021-08-28
Acceptance date: 2021-09-08
Online publication date: 2021-11-02
Publication date: 2022-01-20
Journal of Theoretical and Applied Mechanics 2022;60(1):3–16
KEYWORDS
nonlinear coupled vibrationnonlinear van der Waals forceMultilayer GrapheneSheetselliptical functionexact solution
TOPICS
ABSTRACT
This paper presents a simple exact solution for coupled nonlinear free vibration analysis of
Multilayer Graphene Sheets (MLGS) using elliptical functions. Though elliptical functions
are used in nonlinear dynamics, they are employed to find the exact solution of a coupled
system for the first time. The nonlinear dynamic equation including geometric nonlinearity
and Eringen nonlocal theory is uncoupled by elliptical functions, and exact solutions for
simply supported boundary conditions are obtained. The results are compared with the
harmonic balance method. The nonlinear frequency of MLGS is studied for its effects with
a small scale parameter, and the linear and nonlinear van der Waals force.
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