Fundamental and subharmonic resonances in a nonlinear oscillator with bifurcating modes

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The fundamental and subharmonic resonances of a discrete oscillator with cubic stiffness nonlinearities and linear viscous damping are examined using a multiple-scales averaging analysis. The system is in a '1-1' internal resonance, i.e., it has two equal linearized eigenfrequencies, and possesses nonlinear normal modes. For weak coupling stiffnesses the internal resonance gives rise to a Hamiltonian Pitchfork bifurcation of normal modes which in turn affects the topology of the fundamental and subharmonic resonance curves. It is shown that the number of resonance branches differs before and after the mode bifurcation, and that jump phenomena are possible between forced modes. Some of the steady state solutions were found to be very sensitive to damping: a whole branch of fundamental resonances was eliminated even for small amounts of viscous damping, and subharmonic steady state solutions were shifted by damping to higher frequencies.

Original languageEnglish (US)
Title of host publicationRecent Advances in Structural Mechanics - 1991
PublisherPubl by ASME
Pages13-19
Number of pages7
Volume225
ISBN (Print)0791808998
StatePublished - 1991
EventWinter Annual Meeting of the American Society of Mechanical Engineers - Atlanta, GA, USA
Duration: Dec 1 1991Dec 6 1991

Other

OtherWinter Annual Meeting of the American Society of Mechanical Engineers
CityAtlanta, GA, USA
Period12/1/9112/6/91

ASJC Scopus subject areas

  • Industrial and Manufacturing Engineering
  • Mechanical Engineering

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