Nonlinear Vibrations and Potential Instabilities of a Nanochassis Traveling a Route with Arbitrarily Tiny Irregularities

Free vibrations of axially moving beam-like nanostructures have been investigated in recent years; however, vibrations of moving nanochassis traveling over a surface with arbitrarily small irregularities have not been displayed yet due to some complexities in modeling. To address this challenge, a nonlinear, nonlocal surface energy-based composite beam-like model is established to fairly accurately capture the nanochassis’ vibrations. The nanocar consists of a composite-like nanochassis and the ends’ wheels, where the nanochassis is modeled by an appropriate beam model and the wheels are simulated as rigid solid elements that are attached to the beam’s ends. Both differential- and integral-based formulations are presented, and their nonlinear stiffness, as well as the procedure for capturing the nonlocal elastic field, is carefully explained using the assumed mode approach. For several particular cases, the predicted results by the suggested models are verified with those of several analytical solutions, and reasonably good agreements are achieved. Beyond the aforementioned comparison studies, the possible instabilities of the nanochassis that travels over a straight route were also identified and explained under a small deformation regime. Through conducting a fairly comprehensive parametric study, the roles of amplitude and frequencies of the harmonic route, axial velocity, length, diameter, nonlocality, surface energy, and geometrical nonlinearity on maximum deformations and internal forces are examined comprehensively. This study could be considered as basic scrutiny for the nonlinear analysis of more complex traveling nanostructures over arbitrarily shaped surfaces.