Synchronized periodic solutions of a class of periodically driven nonlinear oscillators

Gamal M. Mahmoud, Tassos Bountis

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


We consider a class of parametrically driven nonlinear oscillators: x+k1x+k2f(x,x)P(Ωt)=0, P(Ωt+2π)=P(Ωt) (*) which can be used to describe, e.g., a pendulum with vibrating length, or the displacements of colliding particle beams in high energy accelerators. Here we study numerically and analytically the subharmonic periodic solution of (*), with frequency 1/ m≅√k1, m=1,2,3,.... In the cases of f(x, x)=x3 and f(x,x)=x4, with P(Ωt)=cost, all of these so-called synchronized periodic orbits are obtained numerically, by a new technique, which we refer to here as the indicatrix method. The theory of generalized averaging is then applied to derive highly accurate expressions for these orbits, valid to the second order in k2.

Original languageEnglish
Pages (from-to)721-728
Number of pages8
JournalJournal of Applied Mechanics, Transactions ASME
Issue number3
Publication statusPublished - Sep 1988
Externally publishedYes

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials

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