Effect of Deformation Shape Modes on Frequency Response of Viscoelastic Couple DLAGS in Thermal Field

In this study, vibration analysis of the coupled system of double-layered annular graphene sheets (CSDLAGSs)resting on a Visco-Pasternak foundation are investigated. Visco-Pasternak model is considered to simulatethe interaction between the DLAGSs and the surrounding elastic medium. The van der Waals (vdW) forces between thetwo layers of annular graphene sheets are taken into account. Using nonlinear strain-displacement relations andnonlocal elasticity orthotropic plate theory, the motion equations are derived based on energy method and Hamilton'sprinciple. In this study for the first time DQM is applied to discretize the motion equations in three direction ofcylindrical coordinate system, which are then solved to obtain the nonlinear frequency of the coupled system for fourtypical deformation modes, namely, (i) in phase-in phase-in phase vibration, (ii) in phase-out of phase-in phasevibration, (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 effects of the nonlinear frequency ratio in the differentmode shape of sheets for different aspect ratio and elastic medium. The result of this study can be useful to design ofmicro electro mechanical systems and nano electro mechanical systems.

Keywords:

DLAGS , Visvo-Pasternak medium , nonlinear vibration