Nanoscale flow-induced nonlinear vibration of multilayer graphene based-resonators: Slip and transition flow regimes

Abstract

This paper presents a nanoscale fluid-structure interaction (FSI) model for flow-induced nonlinear vibration of multilayer graphene based-resonators in the slip and transition regimes. Based on the multibeam interlayer shear model with von Kármán geometric nonlinearity and nonlocal modified couple stress theory, the size-dependent equations of motion are obtained for beam resonators laminated of NG-graphene layer and (NG−1) interlayer crosslinks. The small-scale effect on effective viscosity and slip boundary conditions of nanoscale flow is formulated by introducing the average velocity correction factor. For unbounded and bounded (by a rigid wall) nanoflows, the closed-form expressions of velocity correction factor in terms of Knudsen number, as a dimensionless discriminant parameter, are developed to correct the pressure distribution predicted by the potential theory. The present FSI model considers the size effects through the length scale parameter for microstructure local rotation, the nonlocal parameter for long-range interatomic interactions, and Knudsen number for slip condition of nanoscale flow. The Galerkin's method in conjunction with the multiple-scale perturbation technique is used to obtain closed-form solutions of frequency ratio and time-history response. The natural frequencies of cantilever multilayer graphene nanostrips are validated with the ones existing in the literature. Parametric studies are carried out to investigate the influences of small-scale, number of layers, interlayer shear modulus, and fluid characteristics on the linear and nonlinear natural frequencies. Findings show that the critical upstream speed for dynamic instability of the coupled system can change considerably by taking into account the size effects of nanoflow and nanostructures. Therefore, the classical FSI model is inadequate for analyzing nanoscale flow-induced vibration of nanoresonators. Also, it is seen that the effect of geometric nonlinearity becomes very significant for multilayer graphene beams with small interlayer shear modulus.