Resonances and chaos of electrostatically actuated arch micro/nanoresonators with time delay velocity feedback

Abstract

Abstract Time-delay velocity feedback is introduced into micro- and nano-electro-mechanical systems (M/NEMS). First, the multi-scale method is used to obtain the amplitude-frequency response equation of the system under the influence of delay parameters. The numerical simulation method is used to verify the conclusion. Second, the Melnikov function method is extended to the time-delay system and is used to obtain the chaotic amplitude threshold of the system. Through the Hopf bifurcation condition of the time-delay feedback system, the range of control parameters suitable for the Melnikov function method is obtained, and then, the critical conditions for the chaotic motion of the system are given. Finally, the fourth-order Runge–Kutta method, point-mapping method and spectrum diagram are used to numerically simulate the evolution of the dynamic behaviour of the time-delay controlled system with time delay parameters. The results show that under the condition of a positive gain coefficient and a small amount of delay, the feedback of time delay can effectively restrain the amplitude and chaos of the system. However, under negative feedback, the delayed feedback induces chaotic motion of the system instead. This result shows that time-delay velocity feedback is a good method for the control system. Therefore, reasonable selection of control system parameters can improve the efficiency of vibration control, thus laying the foundation for further study on the vibration of the more complex micro-nano system.