Nonlinear dynamics of a system of coupled oscillators with essential stiffness nonlinearities

Alexander F. Vakakis, Richard H. Rand

Research output: Contribution to conferencePaperpeer-review

Abstract

We study the resonant dynamics of a two-degree-of-freedom system composed a linear oscillator weakly coupled to a strongly nonlinear one, with an essential (nonlinearizable) cubic stiffness nonlinearity. For the undamped system this leads to a series of internal resonances, depending on the level of (conserved) total energy of oscillation. We study in detail the 1:1 internal resonance, and show that the undamped system possesses stable and unstable synchronous periodic motions (nonlinear normal modes - NNMs), as well as, asynchronous periodic motions (elliptic orbits - EOs). Furthermore, we show that when damping is introduced certain NNMs produce resonance capture phenomena, where a trajectory of the damped dynamics gets 'captured' in the neighborhood of a damped NNM before 'escaping' and becoming an oscillation with exponentially decaying amplitude. In turn, these resonance captures may lead to passive nonlinear energy pumping phenomena from the linear to the nonlinear oscillator. Thus, sustained resonance capture appears to provide a dynamical mechanism for passively transferring energy from one part of the system to another, in a one-way, irreversible fashion. Numerical integrations confirm the analytical predictions.

Original languageEnglish (US)
Pages1209-1220
Number of pages12
DOIs
StatePublished - 2003
Event2003 ASME Design Engineering Technical Conferences and Computers and Information in Engineering Conference - Chicago, IL, United States
Duration: Sep 2 2003Sep 6 2003

Other

Other2003 ASME Design Engineering Technical Conferences and Computers and Information in Engineering Conference
Country/TerritoryUnited States
CityChicago, IL
Period9/2/039/6/03

ASJC Scopus subject areas

  • Engineering(all)

Fingerprint

Dive into the research topics of 'Nonlinear dynamics of a system of coupled oscillators with essential stiffness nonlinearities'. Together they form a unique fingerprint.

Cite this