Primary Resonance and Simulation of Coupled Circuit and Microbeam System

In order to study on nonlinear vibration of coupled RLC circuit and microbeam system, a mathematical model of coupled RLC circuit and microbeam system is established and vibration equation of microbeam under discharge state is derived according to the Lagrange-Maxwell equation. Based on multiple scales method for nonlinear vibrations, the first approximation solutions and corresponding to steady state solutions of the primary resonance system are obtained. Results of numerical analyses show that the amplitude of the system increase with increasing voltage and plate length, while they decrease with increasing plate distance or system dumping. With the increasing of voltage or plate length and decreasing of plate distance or system dumping, resonant regions of amplitude frequency response curves enlarge. Using the simulink tool box of MATLAB software, dynamic simulation of the primary resonance system under the discharge state is as follows. It concludes that the system is stable based on analyses of the vibration diagram.