Nonlinear free vibration of graphene platelets reinforced composite corrugated plates

Abstract

The nonlinear vibration of graphene platelets reinforced composite corrugated (GPRCC) rectangular plates with shallow trapezoidal corrugations is investigated. Since graphene platelets are prone to agglomeration, a multi-layer distribution is adopted here to match the engineering requirements. Firstly, an equivalent composite plate model is obtained, and then nonlinear equations of motion are derived by the von Kármán nonlinear geometric relationship and Hamilton’s principle. Afterwards, the Galerkin method and harmonic balance method are used to obtain an approximate analytical solution. Results show that the unit cell half period, unit cell inclination angle, unit cell height, graphene platelet dispersion pattern and graphene platelet weight fraction and geometry play important roles in the nonlinear vibration of the GPRCC plates.

Keywords

corrugated composite plate / graphene platelets / nonlinear vibration / Galerkin method / Harmonic balance method

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