多源激励非线性隔振系统多时滞反馈控制动态特性

The Dynamic Characteristics of Nonlinear Vibration System with Multi-frequencies Excitation and Multi-time-delayed Feedback Control

为了分析多个延时时间对非线性隔振系统的影响,建立了多源激励下非线性隔振多时滞反馈控制系统数学模型。通过数学变换得到了系统的特征方程,由于特征方程是超越函数方程,只考虑含有两个反馈延时时间的情况,得到了不同条件下影响系统稳定性的临界延迟时间。结果表明,当系统方程为自治系统时,延迟较小时系统的响应具有收敛特征;延迟较大时系统不稳定。当系统在多源激励下时,在延迟较小的条件下,系统处于周期振动状态;而当延迟较大时,系统进入混沌状态。

The nonlinear vibration isolation system model with multi-frequencies excitation and multi-time-delayed feedback controlling is established. The characteristic equation of the system is obtained through mathematical transformation. Since the characteristic equation is the transcendental function,the system comprising two-time-delay is considered,the critical delay time correlated to the stability of the system under different conditions is calculated approximately. It is shown that when the system is considered as an autonomous system,the system converges to zero if the delay time is small,and diverges if delay time becomes larger. When the system comprised multi-frequencies excitation,the system exhibits periodic motion for the small delay time,and chaotic vibration for larger delay time.