Normal modes and global dynamics of a two-degree-of-freedom non-linear system-I. Low energies

A. F. Vakakis, R. H. Rand

Research output: Contribution to journalArticlepeer-review

Abstract

The global dynamics of an undamped, strongly non-linear, two-degree-of-freedom system are analyzed by means of Poincaré maps. The oscillator under consideration contains "similar" non-linear normal modes and at certain values of its structural parameters a mode bifurcation is possible. The effect of this bifurcation on the global dynamics is investigated by numerical and analytical techniques. For low energies, a homoclinic orbit exists in the Poincaré map, and is approximately analyzed by the two-variable expansion method. This homoclinic orbit is exclusively caused by the similar mode bifurcation, and as shown in a companion paper [A.K. Vakakis and R.H. Rand, Int. J. Non-Linear Mech. 27, 875-888 (1992)] it gives rise to large-scale chaotic motions when the energy is increased.

Original languageEnglish (US)
Pages (from-to)861-874
Number of pages14
JournalInternational Journal of Non-Linear Mechanics
Volume27
Issue number5
DOIs
StatePublished - Sep 1992

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

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