期刊
ARCHIVE OF APPLIED MECHANICS
卷 86, 期 6, 页码 1083-1094出版社
SPRINGER
DOI: 10.1007/s00419-015-1080-x
关键词
Modal interaction; Mode complexity; Damping; Dissipation; Nonlinear normal modes; Multiple scales
类别
资金
- German Academic Exchange Service within the P.R.I.M.E. program
It is well known that nonlinearity may lead to localization effects and coupling of internally resonant modes. However, research focused primarily on conservative systems commonly assumes that the near-resonant forced response closely follows the autonomous dynamics. Our results for even a simple system of two coupled oscillators with a cubic spring clearly contradict this common belief. We demonstrate analytically and numerically global effects of a weak local damping source in a harmonically forced nonlinear system under condition of 1:3 internal resonance: the global motion becomes asynchronous, i.e., mode complexity is introduced with a non-trivial phase difference between the modal oscillations. In particular, we show that a maximum mode complexity with a phase difference of is attained in a multi-harmonic sense. This corresponds to a transition from generalized standing to traveling waves in the system's modal space. We further demonstrate that the localization is crucially affected by the system's damping. Finally, we propose an extension of the definition of mode complexity and mode localization to nonlinear quasi-periodic motions and illustrate their application to a quasi-periodic regime in the forced response.
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