Nonlinear vibration analysis of visoelastically coupled DLAGS-systems

Nonlinear vibration analysis of the coupled system of double-layered annular graphene sheets (CS-DLAGSs) resting on a Visco-Pasternak foundation is carried out. The two DLAGSs are coupled by an enclosing viscoelastic medium which is simulated as a Visco-Pasternak foundation. The van der Waals (vdW) forces between the two layers of annular graphene sheets are taken into account. Using nonlinear strain-displacement relations and nonlocal elasticity orthotropic plate theory, the motion equations are derived based on energy method and Hamiltonʹs principle. The differential quadrature method (DQM) is applied to discretize the motion equations, which are then solved to obtain the nonlinear frequency of the coupled system for four typical deformation modes, namely, (i) in phase-in phase-in phase vibration, (ii) in phase-out of phase-in phase vibration, (iii) out of phase-in phase-out of phase vibration and (IV) out of phase-out of phase-out of phase vibration. The detailed parametric study is conducted, focusing on the combined effects of the nonlocal parameter, aspect ratio, elastic medium coefficients on the frequency of the CS-DLAGSs. Numerical results indicate that the scale coefficient effect in the case of (i) is higher than that in the other cases. The results are in good agreement with the previous researches.