PRIMARY RESPONSE OF MICRO-BEAM SYSTEM SUBJECTED TO NARROW-BAND RANDOM EXCITATION

To study the primary resonance of series circuit and a micro-beam coupling system subjected to a narrow-band random excitation, the stochastic differential equation of the micro-beam system is established. The frequency response equation of the primary resonance system is obtained based on the method of multiple scales. Ito stochastic differential equation of the system is derived. The steady state response of first order and second order moments of the system are obtained by means of moment method. The influence of the system parameters on the response of the micro-beam is analyzed. 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. The numerical simulation shows that: with the increase of the bandwidth, the thickness of the limit cycle of the phase plot is increased; when the width, thickness and length of the plate are increased, the second order response of the system is increased; when the damping coefficient, the axial force and the distance between the two plates are increased, the second order response of the system is decreased.