Quasi-periodic response regimes of linear oscillator coupled to nonlinear energy sink under periodic forcing
Quasi-periodic response regimes of linear oscillator coupled to nonlinear energy sink under periodic forcing
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DOI：
10.1115/1.2198546
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发表时间：
2007-03
期刊：
影响因子：
--
通讯作者：
O. Gendelman;Y. Starosvetsky
中科院分区：
文献类型：
--
作者：
O. Gendelman;Y. Starosvetsky
本文用解析方法和数值方法研究了外正弦力作用下质量相对较小的非线性能量槽线性振荡器在主共振（1:1）附近的准周期响应。结果表明，在确定的外力幅频范围内，系统表现出准周期响应。揭示了两种性质不同的拟周期响应。第一种是振荡的稳态状态的线性不稳定性的结果。第二种是由于动态流动与系统的阻尼-强迫非线性法向模态的不变流形相互作用，导致流动在该模态附近发生滞回运动。采用简化解析模型对引起拟周期响应的外强迫参数进行了预测。该模型还可以预测在一定阻尼系数范围内出现稳定的准周期状态。所有简化分析模型的结果都得到了数值验证，并观察到相当大的一致性。
Quasi-periodic response of a linear oscillator attached to nonlinear energy sink with relatively small mass under external sinusoidal forcing in a vicinity of main (1:1) resonance is studied analytically and numerically. It is shown that the quasi-periodic response is exhibited in well-defined amplitude-frequency range of the external force. Two qualitatively different regimes of the quasi-periodic response are revealed. The first appears as a result of linear instability of the steady-state regime of the oscillations. The second one occurs due to interaction of the dynamical flow with invariant manifold of damped-forced nonlinear normal mode of the system, resulting in hysteretic motion of the flow in the vicinity of this mode. Parameters of external forcing giving rise to the quasi-periodic response are predicted by means of simplified analytic model. The model also allows predicting that the stable quasi-periodic regimes appear for certain range of damping coefficient..All findings of the simplified analytic model are verified numerically and considerable agreement is observed.