Three-to-one internal resonances in a general cubic non-linear continuous system

Pakdemirli M., Özkaya E.

Journal of Sound and Vibration, vol.268, no.3, pp.543-553, 2003 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 268 Issue: 3
  • Publication Date: 2003
  • Doi Number: 10.1016/s0022-460x(03)00364-x
  • Journal Name: Journal of Sound and Vibration
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.543-553
  • Manisa Celal Bayar University Affiliated: Yes

Abstract

A general continuous system with an arbitrary cubic non-linearity is considered. The non-linearity is expressed in terms of an arbitrary cubic operator. Three-to-one internal resonance case is considered. A general approximate solution is presented for the system. Amplitude and phase modulation equations are derived. Steady state solutions and their stability are discussed in the general sense. The sufficiency condition for such resonances to occur is derived. Finally the algorithm is applied to a beam resting on a non-linear elastic foundation.