Effect of damping on nonlinear forced vibration response of graphene-based nanocomposites

In this study, the nonlinear responses of graphene-based nanocomposite to harmonic resonances have been discussed. This paper presents results of a study aimed at representing dynamic interactions in nanocomposite with simultaneous consideration of geometrical nonlinearity and energy damping effect by viscoelastic medium and internal damping. Based on nonlocal elasticity theory and invoking the nonlinear von Karman strain- displacement relations, the nonlinear governing equation is extracted using the Hamilton principle. To reduce the equation of motion to a nonlinear ordinary differential equation, the Galerkin’s procedure is implemented; then using the multiple scale method, the obtained equation is solved analytically to assess the closed form nonlinear amplitude-frequency relations relevant to graphene with simply supported boundary conditions under harmonic excitation. The detailed parametric study is conducted, focusing on the series effects of nonlocal parameter, aspect ratio and both damping coefficients (internal and external), and frequency of excitation load. The outcomes show a hardening nonlinearity effect for the primary resonance as well as illustrate some phenomena different from the linear vibration