Some results on the dynamics of the linear parametric oscillator with general time-varying frequency

Panayotis D. Kourdis, Alexander F Vakakis

Research output: Contribution to journalArticlepeer-review

Abstract

The dynamics of single-degree-of-freedom linear oscillators under parametric excitation of general type (periodic or non-periodic) is considered. An analytical approach based on complexification and amplitude-phase decomposition of the response is developed leading to an (exact) set of first-order ordinary differential equations governing the amplitude and phase of the motion. Perturbation schemes for solving this set are developed and the solutions of the derived modulation equation are outlined. In addition, some results and comments on the stability of the derived solutions are provided.

Original languageEnglish (US)
Pages (from-to)1235-1248
Number of pages14
JournalApplied Mathematics and Computation
Volume183
Issue number2
DOIs
StatePublished - Dec 15 2006

Keywords

  • Non-periodic parametric excitation
  • Stability

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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