Strongly modulated response in forced 2DOF oscillatory system with essential mass and potential asymmetry
- 作者：Y. Starosvetsky ; O.V. Gendelman
- 关键词：Nonlinear energy sink ; Strongly modulated response ; Relaxation oscillations
- 刊名：Physica D
- 出版年：2008
- 期刊代码：55_01672789
- 类别：ph
- 出版时间：1 August 2008
- 卷：237
- 期：13
- 页码：1719-1733
- 文件大小：2134 K
摘要
Dynamic responses of a linear oscillator coupled to a nonlinear energy sink (NES) under harmonic forcing in the regime of 1:1:1 resonance are investigated. Primary attention is paid to the detailed investigation of the so-called strongly modulated response (SMR), which is not related to the fixed points of average modulation equations of the system. Essential mass asymmetry allows a global analysis of the responses despite strong nonlinearity. It is demonstrated that the strongly modulated response is related to a relaxation-type motion and its description in the limit of small mass ratio maybe reduced to the 1D return map of a subset at a fold line of slow invariant manifold. The SMR exists in the <a name="mml60">a><a style="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6TVK-4RNR6VC-1&_mathId=mml60&_user=1067359&_cdi=5537&_rdoc=3&_acct=C000050221&_version=1&_userid=10&md5=6574ac78669caf73a4e577a0c46e19ce" title="Click to view the MathML source" alt="Click to view the MathML source">O(ε)a>-vicinity of the exact resonance, where <a name="mml61">a><a style="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6TVK-4RNR6VC-1&_mathId=mml61&_user=1067359&_cdi=5537&_rdoc=3&_acct=C000050221&_version=1&_userid=10&md5=c9355fbc47a18ef065b70fd98229cb87" title="Click to view the MathML source" alt="Click to view the MathML source">ε
a.gif" alt="much less-than" title="much less-than" border="0">1a> characterizes the mass asymmetry. It is also shown that the SMR appears in the system as a result of global fold bifurcation of limit cycles and exhibits some properties pertinent to generic 1D nonlinear maps, such as period doubling. Transient responses with finite number of relaxation cycles and subsequent attraction to stable periodic attractor are revealed. Analytic results are compared to numeric simulations and a good agreement is observed.