Abstract:

Taking solenoid switch system as the study object, the electric circuit and magnetic circuit coupled system of the strong nonlinear vibration problem under narrow-band excitation is investigated. The stochastic differential equation of the solenoid switch system subjected to narrow-band excitation is established. The frequency response equation of the system is obtained based on the method of modified multiple scales method, The stability of the primary resonance of the system under narrow band excitation is calculated, and the influence of the parameters of the system on the mean square value of the system is analyzed. The results show that the mean square value of the primary resonance of the system reduces with increasing of the damping coefficient; The mean square value of the primary resonance of the system increases with increasing of the excitation voltage amplitude; The mean square value of the primary resonance of the system reduces with increasing of the resistance; The change of limit cycle of the system is small with increasing of the intensity of the random disturbance.

摘要：

以电磁开关系统为研究对象，研究电路与磁路耦合系统在有界窄带激励下的强非线性振动问题。建立电磁开关强非线性系统在有界窄带激励下的随机微分方程。应用改进的多尺度法得到系统的幅频响应方程，对窄带激励下系统主共振的稳定性进行计算，并分析系统各参数对系统主共振均方值的影响。结果表明，增大阻尼系数可以减小系统主共振的均方值；增大激励电压可以增大系统主共振的均方值；增大电阻可以减小系统主共振的均方值；增大随机扰动强度，极限环变化不大。

关键词: 振动与波, 电磁开关, 改进多尺度法, 窄带激励, 均方值, 强非线性振动