Rogerson, GA, Iandrianov, IV and Danishevskyy, VV ORCID: 0000-0002-3049-4721 (2018) Internal Resonances And Modes Interactions In Non-linear Vibrations Of Viscoelastic Heterogeneous Solids. Journal of Sound and Vibration, 433. ISSN 0022-460X

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The aim of the paper is to study how viscous damping influences mode coupling in non-linear vibrations of microstructured solids. As an illustrative example, natural longitudinal vibrations of a layered heterogeneous medium are considered. The macroscopic dynamic equation is obtained by asymptotic homogenisation. The input continuous problem is analysed using a spatial discretisation procedure. An asymptotic solution is developed by the method of multiple time scales and the fourth-order Runge-Kutta method is employed for numerical simulations. Internal resonances and energy transfers between the vibrating modes are predicted and analysed. The conditions for possible truncation of the original infinite system are discussed. The obtained numerical and analytical results are in good agreement.

Item Type: Article
Additional Information: This is the author accepted manuscript (AAM). The final published version of record is available via Elsevier at - please refer to any terms and conditions of use of the publisher.
Uncontrolled Keywords: Non-linear vibrations; Internal resonances; Modes coupling; Dissipation; Microstructure; Homogenisation; Multiple time scales
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Natural Sciences > School of Computing and Maths
Depositing User: Symplectic
Date Deposited: 21 Jun 2018 15:34
Last Modified: 24 Aug 2018 09:51

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