University of Illinois Urbana-Champaign

Dynamic instabilities in a system with geometrically nonlinear damping and stiffness

Andersen, David K.

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Andersen_David.pdf

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https://hdl.handle.net/2142/26145

Description

Title
Dynamic instabilities in a system with geometrically nonlinear damping and stiffness
Author(s)
Andersen, David K.
Issue Date
2011-08-25T22:16:11Z
Director of Research (if dissertation) or Advisor (if thesis)
  • Vakakis, Alexander F.
  • Bergman, Lawrence A.
Department of Study
Mechanical Sci & Engineering
Discipline
Mechanical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
M.S.
Degree Level
Thesis
Date of Ingest
2011-08-25T22:16:11Z
Keyword(s)
  • Continuous Resonance Scattering
  • Nonlinear Energy Sink
  • Targeted Energy Transfer
Abstract
The dynamics of a system of coupled oscillators possessing strongly nonlinear stiffness and damping is examined. The system consists of a linear oscillator coupled to a strongly nonlinear, light attachment, where the nonlinear terms of the system are realized due to geometric effects. It is shown that the effects of nonlinear damping are far from being purely parasitic and introduce new dynamics when compared to the corresponding systems with linear damping. The dynamics is analyzed by performing a slow/fast decomposition leading to slow flows, which, in turn, are used to study transient instability caused by a bifurcation to 1:3 resonance capture. In addition, a new dynamical phenomenon of continuous resonance scattering is observed that is both persistent and prevalent for the case of the nonlinearly damped system. For certain moderate excitations the transient dynamics ‘tracks’ a manifold of impulsive orbits, in effect transitioning between multiple resonance captures over definitive frequency and energy ranges. Eventual bifurcation to 1:3 resonance capture generates the dynamic instability, which is manifested as a sudden high amplitude burst of the response of the light attachment. Such instabilities that result in strong energy transfer indicate potential for various applications of nonlinear damping such as in vibration suppression and energy harvesting.
Graduation Semester
2011-08
Permalink
http://hdl.handle.net/2142/26145
Copyright and License Information
Copyright 2011 David K. Andersen

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