Analytical solution for nonlinear dynamic behavior of viscoelastic nano-plates modeled by consistent couple stress theory

Abstract

This paper analyses the non-stationary free vibration and nonlinear dynamic behavior of the viscoelastic nano-plates. For this purpose, a sizedependent 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 nanoplates 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 forthorder 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 forceresponses 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.

Dynamic Response Analysis of a Forced Fractional Viscoelastic Beam ∗

“…In [20], the precise integration method (PIM) is extended to numerically integrate the equation of motion with fractional terms, which offers high accuracy and obtained numerical results indicate the viscoelastic dampers can enhance the seismic performance of structures significantly. In [21], the nonstationary free vibration and nonlinear dynamic behavior of the viscoelastic nanoplates are analyzed. Obtained results show that the viscoelastic modelbased vibration is nonstationary unlike the elastic model.…”

Nanostructural Members in Various Fields: A Literature Review

“…Ajri et al [60] studied the non-stationary free vibration and nonlinear behaviour of the viscoelastic nanoplates by employing the consistent couple stress theory. The plate material obeyed the Leaderman integral constitutive relation.…”

An asymptotic consistent couple stress theory for the three‐dimensional free vibration analysis of functionally graded microplates resting on an elastic medium

“…Patel et al 37 used the CCST in conjunction with a simplified moment‐curvature relation to examine the large deflection behavior of microbeams. Ajri et al 38 conducted a nonlinear dynamic analysis of viscoelastic nanoplates using a CCST‐based classical shell theory. Based on the CCST‐based Love's thin shell theory, Dehkordi and Beni 39 and Razavi et al 40 examined the coupled electro‐mechanical free vibration behavior of single‐walled piezoelectric/flexoelectric nanocones and conducted a free vibration analysis of FG piezoelectric nanoshells, respectively.…”