Abstract
The collective nonlinear dynamics of a coupled array of nanocantilevers is investigated while tak- ing into account the main sources of nonlinearities. The amplitude and phase equations of this device, subject to parametric and internal resonances, are analytically derived by means of a multi-modal Galerkin discretiza- tion coupled with a multiscale analysis. Based on the steady-state solutions of these equations, the frequency responses are numerically computed for a two-beam array. The effects of different parameters are investigated and several dynamical aspects are confirmed by numerical simulations. Particularly, we have demonstrated that the bifurcation topology transfer is imposed by the first nanocantilever and it can be general to the collective nonlinear dynamics of the NEMS array.
Highlights
Extensive researches have been conducted, for several years, in order to investigate the microelectromechanical systems (MEMS)
It is due to the fact that the equation of motion of the first beam contains the nonlinear electrostatic terms derived from the Taylor series expansion of the actuation force up to the fifth-order
This illustrates the property of the bifurcation topology transfer between the nanoelectromechanical systems (NEMS) imposed by the first nanocantilever
Summary
Extensive researches have been conducted, for several years, in order to investigate the microelectromechanical systems (MEMS). The principal developed nanoelectromechanical systems include nanowires, carbon nanotubes, silicon nano-beams and nanocantilevers [1]. A NEMS oscillator has a multitude of nonlinear properties such as periodic attractors [3], bistability [4], complex dynamics [5] and bifurcation topology [6] It has attracted considerable interest in recent years [7, 8]. 1:1 internal resonance is considered to derive general equations of phase and amplitude modulations for each cantilever These equations are solved numerically in order to investigate the effects of several design parameters on the collective dynamics of the considered device in terms of energy and bifurcation topology transfers
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