时滞对于参数激励系统周期运动的影响

本文以结构物承受周期激励地震波和具有时滞的弹性地基为背景，研究时滞对于结构物振动响应的影响规律。问胚的数学模型是一个非线性参数激励时滞系统，采用中心流形和平均法得到Hopf分岔方程，研究结果表明时滞量对结构物的地震响应有重要影响，它可使响应振幅增大，意味着结构物遭破坏的危险性增大，同时，结果也表明可以通过阻尼控制器克服时滞引起的危险性。最后，对于不同的时滞量，比较理论分析与数值模拟结果基本吻合，说明了本文结果的可靠性。

Effects of Time Delay on Periodic Motions in Nonlinear System with Parametric Excitation

Based on structure subjected to periodic earthquake excitation and elastic support with time delay, effects of time delay on vibration response of the structure are investigated in the present paper. The mathematical model under consideration is a nonlinear system with parametric excitation and time delay. Hopf bifurcating equation is obtained by using the center manifold method and averaging technique. The results show that the time delay has an important effect on the response of the structure for earthquake and it may enlarge the amplitude of the response, which implies the structure is easier to be damaged with the delay increasing. As well as, it is represented that the delay reduced danger may be overcome by damping controller. Finally, the good agreement between the analytical analysis and the numerical simulation for several values of the delay shows the reliability of the obtained results.