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Free Vibration Analysis of Single-Layered Graphene Sheets Based on a Continuum Model

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Author: Jinbao Wang, Meiling Tian, Xiaoqiao He, Zhibo Tang

Abstract: Recent experiments have shown the applicability of single-layered graphene sheets as electromechanical resonators. Here we introduce a nonlinear continuum plate model for the study of linear and nonlinear free vibration properties of single-layered graphene sheets. By this analysis, natural frequencies and the associated mode shapes pertaining to different values of and for single-layered graphene sheets are given. Also, the effects of the aspect ratio on the fundamental frequencies and the associated mode shapes are investigated. The nonlinear relationship between vibration amplitude and frequency are analyzed in the neighborhood of a given frequency. Parts of results are verified well with experimental observations.

Keywords: Single-layered Graphene Sheet; Vibration Properties; Continuum Model

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