Dynamic pull-in instability of multilayer graphene NEMSs: non-classical continuum model and molecular dynamics simulations

M Nikfar and E Taati and M Asghari, ACTA MECHANICA, 233, 991-1018 (2022).

DOI: 10.1007/s00707-021-03114-1

A novel non-classical continuum model for pull-in analysis of multilayer graphene sheets (MLGSs) is developed to consider the effect of shear interaction between layers based on the nonlocal elasticity theory. The equation governing the motion and corresponding boundary conditions of electrostatically actuated MLGSs are obtained based on the nonlocal shear multiplate theory. The Galerkin method along with the first mode shapes for clamped and cantilever MLGSs together with the method of parameter expansion is used to obtain closed-form expressions of the normalized frequency and time history response. In addition, molecular dynamics (MD) simulations are carried out to validate the pull-in voltages predicted by the developed model for both cantilever and clamped MLGSs. According to the presented results, the nonlocal interlayer shear model can significantly reduce the differences between the results of the classical continuum mechanics and molecular dynamics. Finally, parametric studies are implemented to show the effects of number of layers, initial gap, nonlocal parameter, bending- interlayer shear rigidities, and coefficients of the elastic medium. The results indicate that the pull-in voltage of MLGSs changes remarkably with the interlayer shear modulus and the nonlocal parameter. For cantilever MLGSs (contrary to clamped cases), the nonlocal model predicts larger pull-in voltages than the classical continuum theory. Therefore, it can be concluded that the classical continuum model is inadequate for pull- in analysis of electrostatically actuated MLGSs.

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