On the Chaotic Vibrations of Electrostatically Actuated Arch Micro/Nano Resonators: A Parametric Study

Abstract

Motivated by specific applications, electrostatically actuated bistable arch shaped micro-nano resonators have attracted growing attention in the research community in recent years. Nevertheless, some issues relating to their nonlinear dynamics, including the possibility of chaos, are still not well known. In this paper, we investigate the chaotic vibrations of a bistable resonator comprised of a double clamped initially curved microbeam under combined harmonic AC and static DC distributed electrostatic actuation. A reduced order equation obtained by the application of the Galerkin method to the nonlinear partial differential equation of motion, given in the framework of Euler–Bernoulli beam theory, is used for the investigation in this paper. We numerically integrate the obtained equation to study the chaotic vibrations of the proposed system. Moreover, we investigate the effects of various parameters including the arch curvature, the actuation parameters and the quality factor of the resonator, which are effective in the formation of both static and dynamic behaviors of the system. Using appropriate numerical tools, including Poincaré maps, bifurcation diagrams, Fourier spectrum and Lyapunov exponents we scrutinize the effects of various parameters on the formation of chaotic regions in the parametric space of the resonator. Results of this work provide better insight into the problem of nonlinear dynamics of the investigated family of bistable micro/nano resonators, and facilitate the design of arch resonators for applications such as filters.