期刊
NONLINEAR DYNAMICS
卷 98, 期 4, 页码 2755-2773出版社
SPRINGER
DOI: 10.1007/s11071-019-05023-4
关键词
Spectral submanifolds; Model order reduction; Forced response curves; Isolas
We show how spectral submanifold (SSM) theory can be used to provide analytic predictions for the response of periodically forced multi-degree-of-freedom mechanical systems. These predictions include an explicit criterion for the existence of isolated forced responses that will generally be missed by numerical continuation techniques. Our analytic predictions can be refined to arbitrary precision via an algorithm that does not require the numerical solutions of the mechanical system. We illustrate all these results on low- and high-dimensional nonlinear vibration problems. We find that our SSM-based forced response predictions remain accurate in high-dimensional systems, in which numerical continuation of the periodic response is becoming computationally expensive.
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