Response regimes of linear oscillator coupled to nonlinear energy sink with harmonic forcing and frequency detuning
Response regimes of linear oscillator coupled to nonlinear energy sink with harmonic forcing and frequency detuning
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DOI：
10.1016/j.jsv.2007.12.023
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发表时间：
2008-08
影响因子：
4.7
通讯作者：
Y. Starosvetsky;O. Gendelman
中科院分区：
文献类型：
--
作者：
Y. Starosvetsky;O. Gendelman
本文所研究的动力学系统是由受简谐激励的线性振子和附加的非线性能汇组成的。在主共振附近（1：1）的外部强迫频率失谐包括在系统的调查。通过（自适应）平均方法对周期和准周期区域进行了详细的研究。局部分岔的周期性制度的揭示和充分描述的空间中的系统参数（振幅的激励，阻尼和频率失谐）。提出了一种新的预测强调制响应（SMR）的解析方法。与以往的研究结果相反，该方法提供了SMR存在的充分条件。共存的响应制度的各种可能性的预测分析和数值模拟。其中之一是两种不同的定期制度与《最低限度标准》并存。简化的分析模型的所有结果进行了验证数值和相当大的协议观察。
Dynamical system under investigation in the current work is comprised of harmonically forced linear oscillator with attached nonlinear energy sink. External forcing frequency detuning near the main resonance (1:1) is included in the system investigation. The detailed study of the periodic and quasiperiodic regimes is done in the work via (adaptive) averaging method. Local bifurcations of the periodic regimes are revealed and fully described in the space of system parameters (amplitude of excitation, damping, and frequency detuning). Novel analytical approach for predictions of strongly modulated response (SMR) is presented. This approach provides a sufficient condition for the SMR existence contrary to the previous studies. Various possibilities of coexistence of the response regimes are predicted analytically and demonstrated numerically. Among those is a coexistence of two distinct periodic regimes together with the SMR. All findings of the simplified analytic model are verified numerically and considerable agreement is observed.