Limitation on the method of strained coordinates for vibrations with weak grazing unilateral contact

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• 作者：Stéphane Junca ; Ly Tong
• 关键词：Vibration ; Piecewise linear ; Grazing contact ; Perturbation ; Asymptotic analysis ; Lindstedt–Poincaré method ; 34E10 ; (70K75 ; 34E13)
• 刊名：Nonlinear Dynamics
• 出版年：2015
• 出版时间：April 2015
• 年：2015
• 卷：80
• 期：1-2
• 页码：197-207
• 全文大小：848 KB
• 参考文献：1. Jiang, D, Pierre, C, Shaw, SW (2004) Large-amplitude non-linear normal mode of piecewise linear systems. J. Sound Vib. 272: pp. 869-891 CrossRef
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  9. Luongo, A., Zulli, D.: A paradigmatic system to study the transition from zero/hopf to double-zero/hopf bifurcation. Nonlinear Dyn. 70(1), 111-24 (2012)
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• 刊物类别：Engineering
• 刊物主题：Vibration, Dynamical Systems and Control
  Mechanics
  Mechanical Engineering
  Automotive and Aerospace Engineering and Traffic
  
• 出版者：Springer Netherlands
• ISSN：1573-269X

文摘

The nonlinear normal modes have recently been investigated with the method of strained coordinates for spring-mass models with some springs with piecewise linear stiffness. The N d.o.f. case and the mathematical validity of the method for large time were rigorously proved. The time validity is related to the nature of contact. For grazing contact, this method and also the multiscale expansion lose nonlinear features. For a small piecewise linear stiffness, we show that this method is less precise for a weak unilateral grazing contact. Thus, the validity of the asymptotic expansion for large time cannot be improved and the method has to be modified.