Nonlinear Vibration Analysis of Prestressed Double Layered Nanoscale Viscoelastic Plates

Abstract

In the present study, the nonlinear flexural vibration behavior of a double layered prestressed viscoelastic nanoplate under shear in-plane load is investigated based on nonlocal elasticity theory. Using nonlinear strain-displacement relations, the geometrical nonlinearity is modeled. Both nonlocal plate theory and Hamilton’s principle are utilized for deriving the governing equations. The differential quadrature method (DQM) is employed for the computation of nonlinear frequency of the nanoplate. The detailed parametric study is conducted, focusing on the influences of small scale, aspect ratio of the plate, Winkler and Pasternak effects, van der Walls (vdW) interaction, temperature, the effect of pre-stress under shear in-plane load, and the viscidity of the plate. The influence of the viscoelastic coefficient is also discussed. The plots for the ratio of nonlinear to linear frequencies versus maximum transverse amplitude for double layered viscoelastic nanoplate are presented.