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 contribution||Applying the method of normal forms to second order nonlinear vibration problems|
|Pages (from-to)||1141 - 1163|
|Journal||Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences|
|Publication status||Published - 2011|