Random Vibration Of Micro Beam Nonlinear Systems Excited By Voltage

Micro-beam is a typical mechanical and electrical coupling system of MEMS. With the continuous innovation and rapid development of MEMS technology, the accuracy and stability of the micro-beam system have developed into the focus of current research. The design, optimization, stability and controllability of MEMS of their work status are directly impacted by vibration characteristics of the micro-beam. Therefore, it is very significant to study the dynamic characteristics of the coupled system with RLC circuit and the micro-beam under the random voltage excitation.Taking the micro-beam under the action of electric field force as a model, the dynamic vibration equation which coupled mechanic and electric is established baced on Lagrange-Maxwell equation.The characteristics of the micro-beam linear system under the excitation of white noise are solved without considering nonlinear terms. In accordance with the FPK method of nonlinear stochastic vibration theory, to study the response characteristics of the nonlinear system with the white noise excitation.Compared the results of the nonlinear system with the result of the linear system, to shows the conclusion is correct.The primary and parametric resonance of series circuit and micro-beam coupling system are analyzed under the narrow-band random excitation. The stochastic differential equation of the micro-beam system subjected to narrow-band excitation is established.The frequency response equation of the primary and parametric resonance of the system is obtained through the method of multiple scales. Ito stochastic differential equation of system is derived. The first order and second order approximate expressions are obtained through moment method, the influence of the system parameters on the response of the micro-beam is also analyzed. The correctness of numerical analysis is verified with Runge-Kutta method. The results show that the sufficient and necessary conditions for the stability of the primary resonance are the same as the first order and second order moment stability of the system, so one can choose either of them to caculate. Multiple scales method can only solve the problem of system of primary resonance and parametric resonance, and it can not be used to solve the problems of super harmonic resonance and harmonic resonance pressure.RLC circuit with the beam coupled system in a bounded narrow-band excitation primary resonance, internal resonance and primary parametric resonance problems are studied. Approximate expressions for the Ito stochastic differential equation and the random mean square response are derived. Compared with the single micro beam system,the results show that the amplitude and resonance region of the coupled system are increased obviously, and the stability region also changed.