Bifurcation and Chaos in Size-Dependent NEMS Considering Surface Energy Effect and Intermolecular Interactions

Abstract

The impetus of this study is to investigate the chaotic behavior of a size-dependent nano-beam with double-sided electrostatic actuation, incorporating surface energy effect and intermolecular interactions. The geometrically nonlinear beam model is based on Euler-Bernoulli beam assumption. The influence of the small-scale and the surface energy effect are modeled by implementing the consistent couple stress theory proposed by Hadjesfandiari and Dargush together with Gurtin-Murdoch elasticity theory. The governing differential equation of motion is derived using Hamilton's principle and discretized to a set of nonlinear ODE through Galerkin's method. Nonlinearities stemmed from different sources such as mid-plane stretching, electrostatic and interatomic forces lead to an intensive nonlinear dynamics in nano-electro-mechanical devices so that the systems exhibit rich dynamic behavior such as periodic and chaotic motions. Poincaré portrait is utilized in order to present the system dynamic response in discrete state-space. Bifurcation analysis has been performed with a change in the magnitude of AC voltage corresponding to the various values of DC voltage and excitation frequency. Then, we compare some ranges of AC voltage amplitude, in which the system response becomes stable for these cases. Fast Fourier transformation is also carried out to analyze the frequency content of the system response.