Order reduction of nonlinear systems with time periodic coefficients using invariant manifolds

S. C. Sinha, Sangram Redkar, Eric A. Butcher

Research output: Contribution to journalArticle

42 Scopus citations

Abstract

The basic problem of order reduction of nonlinear systems with time periodic coefficients is considered. First, the equations of motion are transformed using the Lyapunov-Floquet transformation such that the linear parts of new set of equations are time invariant. At this stage, the linear order reduction technique can be applied in a straightforward manner. A nonlinear order reduction methodology is also suggested through a generalization of the invariant manifold technique via 'Time Periodic Center Manifold Theory'. A 'reducibility condition' is derived to provide conditions under which a nonlinear order reduction is possible. Unlike perturbation or averaging type approaches, the parametric excitation term is not assumed to be small. An example consisting of two parametrically excited coupled pendulums is given to show potential applications to real problems. Order reduction possibilities and results for various cases including 'parametric', 'internal', 'true internal' and 'combination' resonances are discussed.

Original languageEnglish (US)
Pages (from-to)985-1002
Number of pages18
JournalJournal of Sound and Vibration
Volume284
Issue number3-5
DOIs
StatePublished - Jun 21 2005
Externally publishedYes

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Acoustics and Ultrasonics
  • Mechanical Engineering

Fingerprint Dive into the research topics of 'Order reduction of nonlinear systems with time periodic coefficients using invariant manifolds'. Together they form a unique fingerprint.

  • Cite this