Conference paper
The method of varying amplitudes for solving (non)linear problems involving strong parametric excitation
Parametrically excited systems appear in many fields of science and technology, intrinsically or imposed purposefully; e.g. spatially periodic structures represent an important class of such systems [4]. When the parametric excitation can be considered weak, classical asymptotic methods like the method of averaging [2] or multiple scales [6] can be applied.
However, with many practically important applications this simplification is inadequate, e.g. with spatially periodic structures it restricts the possibility to affect their effective dynamic properties by a structural parameter modulation of considerable magnitude. Approximate methods based on Floquet theory [4] for analyzing problems involving parametric excitation, e.g. the classical Hill’s method of infinite determinants [3,4], can be employed also in cases of strong excitation; however, with Floquet theory being applicable only for linear systems, this is impossible or rather cumbersome for combined parametric and direct excitation, or with nonlinearity.
Language: | English |
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Year: | 2015 |
Proceedings: | IUTAM Symposium on Analytical Methods in Nonlinear Dynamics |
Types: | Conference paper |
ORCIDs: | Sorokin, Vladislav and Thomsen, Jon Juel |