Multistability of the Vibrating System of a Micro Resonator

Abstract

Multiple attractors and their fractal basins of attraction can lead to the loss of global stability and integrity of Micro Electro Mechanical Systems (MEMS). In this paper, multistability of a class of electrostatic bilateral capacitive micro-resonator is researched in detail. First, the dynamical model is established and made dimensionless. Second, via the perturbating method and the numerical description of basins of attraction, the multiple periodic motions under primary resonance are discussed. It is found that the variation of AC voltage can induce safe jump of the micro resonator. In addition, with the increase of the amplitude of AC voltage, hidden attractors and chaos appear. The results may have some potential value in the design of MEMS devices.

Global Bifurcation Behaviors and Control in a Class of Bilateral MEMS Resonators

“…The schematic diagram of a typical bilateral MEMS resonator is depicted in Figure 1. The MEMS resonator consists of the movable electrode and nonlinear electrostatic forces on each side [8,19]. In this system, an external driving force on the resonator is applied by means of electrical driving voltages.…”

“…Ali and Ardeshir [7] modeled a dielectric elastomer resonator as a sandwiched Euler-Bernoulli microbeam and presented multiple periodic responses induced by subcritical bifurcations. Zhu and Shang [8] discussed the phenomenon jump among coexisting multiple periodic attractors in an electrostatic bilateral microresonator. It has been realized that even if MEMS resonators finally vibrate periodically, the phenomenon jump among coexisting multiple periodic attractors is unwanted as it leads to unreliability of work performance of the micro devices.…”

“…Can a control strategy reduce both of them? To answer these questions, we considered a typical bilateral MEMS resonator containing multiple potential wells [8,19], and investigated the mechanisms behind chaos and pull-in instability of MEMS resonators as well as the mechanisms of control strategies on reducing them. The rest of the paper is arranged as follows.…”

Advances in Optimization and Nonlinear Analysis

“…Multiple attractors and their fractal basins of attraction can lead to the loss of global stability and integrity of Micro Electro Mechanical Systems (MEMS). In the paper of Zhu et al [12], multistability of a class of electrostatic bilateral capacitive micro-resonator is researched in detail. First, the dynamical model is established and made dimensionless.…”

Coexisting Attractor in a Gyrostat Chaotic System via Basin of Attraction and Synchronization of Two Nonidentical Mechanical Systems

“…Basins can also play a helpful role in finding hidden and coexisting attractors in chaotic systems [20][21][22][23]. The coexisting attractor (multistability) [24] for a set of parameters has been studied for many nonlinear systems. It identifies the nonuniqueness of the system's final state.…”