Effects of weak nonlinearity on dispersion relations and frequency band-gaps of periodic structures

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dc.contributor.author Sorokin, Vladislav en
dc.contributor.author Thomsen, JJ en
dc.coverage.spatial Florence, Italy en
dc.date.accessioned 2017-08-01T03:53:44Z en
dc.date.issued 2015 en
dc.identifier.citation 22nd International Congress on Sound and Vibration, Florence, Italy, 12 Jul 2015 - 16 Jul 2015. Proceedings of 22nd International Congress on Sound and Vibration. 2843-2849. 2015 en
dc.identifier.isbn 9781510809031 en
dc.identifier.uri http://hdl.handle.net/2292/34659 en
dc.description.abstract The analysis of the behaviour of linear periodic structures can be traced back over 300 years, to Sir Isaac Newton, and still attracts much attention. An essential feature of periodic struc-tures is the presence of frequency band-gaps, i.e. frequency ranges in which waves cannot propagate. Determination of band-gaps and the corresponding attenuation levels is an im-portant practical problem. Most existing analytical methods in the field are based on Floquet theory; e.g. this holds for the classical Hill’s method of infinite determinants, and the method of space-harmonics. However, application of these for nonlinear problems is impossible or cumbersome, since Floquet theory is applicable for linear systems only. Thus the nonlinear effects for periodic structures are not yet fully uncovered, while at the same time applica-tions may demand effects of nonlinearity on structural response to be accounted for. The present work deals with analytically predicting dynamic responses for nonlinear continuous elastic periodic structures. Specifically, the effects of weak nonlinearity on the dispersion re-lation and frequency band-gaps of a periodic Bernoulli-Euler beam performing bending os-cillations are analyzed. Modulation of the beam structural properties is not required to be small or piecewise constant. Various sources of nonlinearity are analyzed, namely, nonlinear (true) curvature, nonlinear inertia due to longitudinal motions of the beam, nonlinear materi-al, and also nonlinearity associated with mid-plane stretching. A novel approach, the Method of Varying Amplitudes, is employed. This implies representing a solution in the form of a harmonic series with varying amplitudes; however, in contrast to averaging methods, the amplitudes are not required to vary slowly in space. As a result, a shift of band-gaps to a higher (or lower) frequency range is revealed, while the width of the band-gaps appears rela-tively insensitive to (weak) nonlinearity. The results are validated by numerical simulation, and explanations of the effects are suggested. en
dc.description.uri https://iiav.org/icsv22/index.php?va=viewpage&vaid=175# en
dc.relation.ispartof 22nd International Congress on Sound and Vibration en
dc.relation.ispartofseries Proceedings of 22nd International Congress on Sound and Vibration en
dc.rights Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher. en
dc.rights.uri https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm en
dc.title Effects of weak nonlinearity on dispersion relations and frequency band-gaps of periodic structures en
dc.type Conference Item en
pubs.begin-page 2843 en
pubs.author-url http://www.proceedings.com/27211.html en
pubs.end-page 2849 en
pubs.finish-date 2015-07-16 en
pubs.start-date 2015-07-12 en
dc.rights.accessrights http://purl.org/eprint/accessRights/RestrictedAccess en
pubs.subtype Proceedings en
pubs.elements-id 625634 en
pubs.org-id Engineering en
pubs.org-id Mechanical Engineering en
pubs.record-created-at-source-date 2017-05-14 en

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