Amplitude motion and frequency simulation of a composite viscoelastic microsystem within modified couple stress elasticity

Abstract

In this research, amplitude motion and frequency simulation of a thick annular microsystem with graphene nanoplatelets (GPL) reinforcement in the framework of the modified couple stress theory (MCST) is undertaken. For obtaining the effective Poisson ratio, and mass density, the role of mixture is employed. As well as this, the Halpin–Tsai micromechanics model is presented for modeling the effective Young module of the current composite microstructure. The mathematical formulations of the current microstructure, size-dependent governing equations and boundary conditions are obtained by considering the MCST’s terms such as higher-order stress tensors, and symmetric rotation gradient into strain energy of the size-dependent GPL reinforced composite (GPLRC) microstructure. Finally, the generalized differential quadrature method (GDQM) is employed to obtain eigenvalue and eigenvectors of the GPLRC microsystem. Afterward, a parametric study is conducted to present the impacts of the radios ratio, length scale parameter, viscoelastic parameter, radial and circumferential mode number, and GPL’s geometry, on the amplitude motion, and frequency characteristics of the GPLRC annular microsystem. The results demonstrate that in the higher value of the radius ratio and time-dependent parameter, we can ignore the influence of length scale parameter on the amplitude and frequency of the annular microsystem. The useful suggestion of this study is that as the thickness of the GPLs increases, the impact of length scale parameter on the frequency of the annular microsystem decreases.