The method of varying amplitudes for solving (non)linear problems involving strong parametric excitation

Vladislav Sorokin, Jon Juel Thomsen

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    Abstract

    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.
    Original languageEnglish
    Title of host publicationProceedings of the IUTAM Symposium on Analytical Methods in Nonlinear Dynamics
    Number of pages2
    Publication date2015
    Publication statusPublished - 2015
    Event IUTAM Symposium on Analytical Methods in Nonlinear Dynamics - Frankfurt, Germany
    Duration: 6 Jul 20159 Jul 2015
    http://iutam.org/iutam-symposium-on-analytical-methods-in-nonlinear-dynamics/

    Conference

    Conference IUTAM Symposium on Analytical Methods in Nonlinear Dynamics
    Country/TerritoryGermany
    CityFrankfurt
    Period06/07/201509/07/2015
    Internet address

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