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In this paper, the nonlinear forced vibration of single layered graphene sheet including the pre-Stressed effect is studied based on nonlocal elasticity theory. The graphene sheet is located on a viscoelastic foundation based on Kelvin-Voigt model and exposed to thermo-magnetic-mechanical loads. A particle with constant velocity and concentrated load moves on the graphene sheet and applies mechanical shock to it. At first, using nonlinear strain-displacement relations, the geometrical nonlinearity is modeled. Besides, nonlocal plate theory and Hamilton's principle are utilized for deriving the governing equation. In the second step, using Galerkin method, the partial differential equation is transformed to the ordinary differential equation. Then, governing equation is solved based on multiple time scales method. Finally, frequency-response equations under sub-harmonic and super-harmonic stimulation are studied. Emphasizing the effect of nonlinearity, the results for the nondimensional nonlinear frequency versus nondimensional amplitude, the nondimensional phase angle and nondimensional velocity for single layered graphene sheet are plotted. At the end, numerical results are compared with results in the other researches. The results emphasize that the velocity of the nano particle and force amplitude are responsible to make resonance in the system based on a SLGS. Besides, force amplitude can be effective to intensify the effect of the mechanical shock in behavior of SLGS. [ABSTRACT FROM AUTHOR]

This article investigates the nonlinear vibration behavior of multiscale nanocomposites nanoshell subjected to hygrothermal environment and resting on elastic foundations. The novelty and contribution of this article is considering a multiscale doubly curved sandwich nanoshell. Three-phase composite nanoshell composes of polymer-Carbon nanotube-fiber (PCF) and polymer-Graphene platelet-fiber (PGF) according to Halpin-Tsai model. Various distributions patterns such as U (uniform), X, A and O are considered. The classical shell theory and nonlocal strain gradient theory including von Kármán strain–displacement relationships are employed to build the size-dependent governing equations. The governing equations of multiscale nanoshell have been implemented by Hamilton's principle and solved by homotopy perturbation method. For investigating correctness and accuracy, this paper is validated by other previous researches. Finally, the effects of different parameters such as temperature rise, various distributions patterns and curvature ratio have been investigated. • Nonlinear vibration behavior of multiscale nanocomposites nanoshell is investigated in hygrothermal environment. • The influence of different parameters such as temperature rise, various distributions patterns, curvature ratio are investigated in detail. • Various distributions patterns such as U (uniform), X, A and O are considered. • Via the classical shell theory and the von Kármán type hypothesis the displacements are expressed. • Nonlocal strain gradient governing equations of multiscale nanoshell have been implemented by employing the Hamilton's principle. • Using the homotopy perturbation method, the equations of motions are solved. • The governing equations of multiscale shell have been derived by implementing Hamilton's principle. [ABSTRACT FROM AUTHOR]