Dynamic instabilities in a system with geometrically nonlinear damping and stiffness

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.

Name thesis:degree_name

M.S.

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Mechanical Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Andersen, David K.

Contributors dc:contributor

• Vakakis, Alexander F.
• Bergman, Lawrence A.

• Continuous Resonance Scattering
• Nonlinear Energy Sink
• Targeted Energy Transfer

Statement dc:rights

• Copyright 2011 David K. Andersen

Language dc:language

en

Handle dc:identifier

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

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/26145