Study On Nonlinear Dynamics Of Micro-electro-mechanical System

Micro-electro-mechanical system is very important. People pay much attention to it and do a lot of research. MEMS has abundant non-linear dynamics phenomena. In order to improve stability and security of operation of these systems, we ought to study these systems in detail.A nonlinear dynamics model of coupled RLC circuit and Micro-beam system is established by means of the Lagrange-Maxwell equation, considering the kinetic energy, the potential energy, the magnetic energy and electrical energy, the dissipation function and the influence of the non-conservative generalized force. Using the nonlinear oscillation theory to analyze micro-beam system, circuit system, multiple modals system of micro-beam and the coupled RLC circuit and micro-beam system. On the analysis of pull-in voltage, a"pull-in"voltage that is the standard for the calculation was acquired. For micro-beam system, with the increasing of capacity distance, nature frequency of the system enlarges; with the increasing of voltage, nature frequency of the system decreases. With changing of the tune value, the amplitudes of primary resonance, sub-harmonic resonance, super-harmonic resonance and parameter resonance can be changed. Changing other parameters, amplitudes of response curves will change correspondingly. The jump phenomenon is found in these systems. For circuit system, the current will achieve a stability after a short of vibration. For multiple resonance, 2:1 interaction resonance can't meet with the condition of nature frequency, 3:1 interaction resonance can't meet with the condition of modals, as a result of that, neither of them happen. Under the condition ofΩ=ωmandωm =ωi+ωj, the condition of nature frequency is satisfied, but the modals can not coupled properly. For the coupled RLC circuit and micro-beam system, two coupled modals are all excited and vibrated; energy is transformed between two modals, but the station is unstable, which will lose its station by a little disturbance. Changing systematic parameters, amplitudes of response curves will change correspondingly. In double resonances conditionω2≈2ω1 and 2Ω≈3ω2, the topology structure of response curves is changed, with the changing of parameters of the system and amplitudes of certain modal can be changed, because interaction resonance restrain 1/3 sub-harmonic resonance and the amplitude of a1 and a 2 has approached to the stabilization. As to the 1/2 sub-harmonic resonance, 2 super-harmonic resonance, 3 super-harmonic resonance, parametric resonance, the same situation happens.The amplitudes of electric poles and current and voltage of the system could be controlled. So the micro-electro-mechanical system is under the safe station.