Abstract This paper analyses the non-stationary free vibration and nonlinear dynamic behavior of the viscoelastic nano-plates. For this purpose, a size-dependent theory is developed in the framework of the consistent couple stress theory for viscoelastic materials. The previously presented modified couple stress theory was based on some consideration making it partially doubtful to apply. This paper uses the recent findings for the mentioned problem and develops it to analyze the nonlinear dynamic behavior of nano-plates with nonlinear viscoelasticity. The material is supposed to follow the Leaderman integral nonlinear constitutive relation. In order to capture the geometrical nonlinearity, the von-Karman strain displacement relation is used. The viscous parts of the size-independent and size-dependent stress tensors are calculated in the framework of the Leaderman integral and the resultant virtual work terms are obtained. The governing equations of motion are derived using the Hamilton principle in the form of the nonlinear second order integro-partial differential equation with coupled terms. These coupled size-dependent viscoelastic equations are solved using the forth-order Runge-kutta and Harmonic balance method after simplifying by the expansion theory. The short-time Fourier transform is performed to examine the system free vibration. In addition, frequency- and force-responses of the nanosystem subjected to distribute harmonic load are presented. The obtained results show that the viscoelastic model-based vibration is non-stationary unlike the elastic model. Moreover, the damping mechanism of the viscoelasticity is amplitude dependent and the contribution of the viscoelastic damping terms at higher forcing conditions becomes noticeable.

AbstractThe paper investigates the effects of application of nonlocal elasticity theory on electromechanical behaviors of single-walled carbon nanotubes under electrostatic actuation. The influences of different dimensions and boundary conditions on the vibration and dynamic instability of the carbon nanotubes are studied, in detail, using this theory. The results reveal that application of the nonlocal elasticity theory leads to the higher pull-in voltages for the nonlocal model applied for carbon nanotubes. Thus, in order to have more accurate results, one should apply nonclassical theorems such as the nonlocal elasticity theory to scrutinize the mechanical and electromechanical behaviors of the nano structures.