Nonlinear resonant behaviors of graphene sheet affixed on an elastic medium considering scale and thermal effects

•Effects of thermal load and scale on the nonlinear resonant of graphene is given.•The anisotropic behavior of graphene induces the nonlinear frequency to increase.•The nonlinear thermal resonant of graphene is controlled by the medium stiffness.

An analytical method is presented to investigate the nonlinear vibration behaviors of graphene sheet affixed on an elastic medium, where small-scale and thermal effects are considered. Based on von Kármán geometrical nonlinear relationship and nonlocal elasticity theory, the nonlinear thermo-vibration equations of monolayer graphene sheet affixed on an elastic medium is derived. Utilizing the global residue harmonic balance method to solve the nonlinear thermo-vibration equations, the nonlinear thermo-resonant frequencies of graphene sheets affixed on an elastic medium with three different boundary conditions are obtained. Results show that small-scale effect has a significant impact on the nonlinear resonant frequency of monolayer graphene sheet and the impact of scale effect gradually decreases with the size of graphene sheet increases. Moreover the nonlinear thermal resonant frequency of monolayer graphene sheet nonlinearly grows with its initial displacement, and the nonlinear characteristics of thermal resonant frequency appear in larger growth rate as thermal loading increases. In addition, the effect of equivalent Winkler modulus and shear modulus of elastic medium on the nonlinear thermal resonant frequency is also described and discussed.

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