摘要
研究电路与微梁耦合系统在有界窄带激励下的主共振问题。建立有界窄带激励下微梁系统的随机微分方程。应用多尺度法得到系统主共振的幅频响应方程,导出系统的Ito随机微分方程,采用矩法得到系统随机均方响应一阶矩和二阶矩的近似表达式。数值分析了系统各个参数对微梁响应的影响。结果表明:主共振稳态解稳定的充分必要条件与系统一阶矩和二阶矩稳定的充分必要条件是一样的;随着带宽的增加,相轨图极限环的厚度增加;当微梁上极板的宽度、厚度和长度增加时,系统二阶矩增大;当上极板的阻尼系数、轴向力以及上下极板间的距离增加时,系统的二阶矩减小。
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.
出处
《工程力学》
EI
CSCD
北大核心
2017年第B06期19-25,共7页
Engineering Mechanics
基金
河北省自然科学基金项目(A200900097)
关键词
微梁
主共振
多尺度法
非线性
窄带激励
micro-beam
primary resonance
method of multiple scales
nonlinear system
narrow-band random excitation
