Applying the method of normal forms to second order nonlinear vibration problems

SA Neild, DJ Wagg

Research output: Contribution to journalArticle (Academic Journal)peer-review

66 Citations (Scopus)

Abstract

Vibration problems are naturally formulated with second-order equations of motion. When the vibration problem is nonlinear in nature, using normal form analysis currently requires that the second-order equations of motion be put into first-order form. In this paper, we demonstrate that normal form analysis can be carried out on the second-order equations of motion. In addition, for forced, damped, nonlinear vibration problems, we show that the invariance properties of the first- and second-order transforms differ. As a result, using the second-order approach leads to a simplified formulation for forced, damped, nonlinear vibration problems.
Translated title of the contributionApplying the method of normal forms to second order nonlinear vibration problems
Original languageEnglish
Pages (from-to)1141 - 1163
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume467
DOIs
Publication statusPublished - 2011

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