时滞非线性动力吸振器的减振机理

MECHANISM ANALYSIS OF DELAYED NONLINEAR VIBRATION ABSORBER

对一个带有时滞非线性动力吸振器的两自由度结构,采用多尺度法研究了时滞非线性动力吸振器对主系统的减振性能,得到了主系统的振幅-时滞响应曲线.研究结果表明,对时滞非线性动力吸振器,可以通过调节反馈增益系数和时滞控制主系统的振动.研究还发现,对确定的反馈增益系数,可以存在时滞的一些调节区域,时滞非线性动力吸振器可以减小主系统的振动.并且在时滞的这些可调区域里,存在一个"最大减振点"对应这一反馈增益系数下主系统振幅的最小值.对不同的反馈增益系数,"最大减振点"对应的主系统的振幅也不同.因此能够找到一组反馈增益系数和时滞量的最佳值,最大程度地减小主系统的振动.研究结果表明,当反馈增益系数和时滞量调到最佳值时,主系统的振动较无时滞非线性动力吸振器可以减少90%左右,数值模拟也证实了解析结果的正确性.

In a two-degree-of-freedom system with delayed nonlinear dynamical vibration absorber, the method of multiple scales is employed to study its performance of vibration suppression. The amplitude-delay response curves of the primary system are obtained. The results show that for the delayed nonlinear dynamical vibration absorber, the gain and the delay may be tuned to control the vibration of the primary system. With the delay varying for a fixed gain, it is easy to see that the vibration can be suppressed at some values of the delay under the conditions that the system is stable. The ＂maximum vibration suppression point＂ may be predicted at which the amplitude of the primary system is the minimum for a fixed gain. For different values of the gain, the amplitudes of the primary system are different at their ＂maximum vibration suppression point＂. Correspondingly, the optimum values of the gain and the delay may be obtained to suppress the amplitude of the primary system to a minimum. The results show that the vibration of the primary system can be suppressed about 90% when the optimum values of the gain and the delay are obtained by comparing with the nonlinear dynamical vibration absorber. All the present analytical predictions are in good agreement with the numerical simulation.