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dc.contributorVirginia Techen_US
dc.contributor.authorNayfeh, Ali H.en_US
dc.date.accessioned2014-04-24T18:34:19Z
dc.date.available2014-04-24T18:34:19Z
dc.date.issued1987-10-01
dc.identifier.citationNayfeh, A. H., "surface waves in closed basins under parametric and internal resonances," Phys. Fluids 30, 2976 (1987); http://dx.doi.org/10.1063/1.866075
dc.identifier.issn1070-6631
dc.identifier.urihttp://hdl.handle.net/10919/47660
dc.description.abstractThe method of multiple scales is used to analyze the nonlinear response of the free surface of a liquid in a cylindrical container to a harmonic vertical oscillation in the presence of a two‐to‐one internal (autoparametric) resonance. Four first‐order ordinary‐differential equations are derived for the modulation of the amplitudes and phases of the two modes involved in the internal resonance with the lower mode is excited by a principal parametric resonance. In the presence of small damping, the long‐time response may be any of (a) a trivial motion, (b) a limit cycle involving both modes, (c) an amplitude‐ and phase‐modulated sinusoid (motion on a two torus), and (d) a chaotically modulated sinusoid.
dc.description.sponsorshipNSF MSM-8521748
dc.format.mimetypeapplication/pdfen_US
dc.language.isoen_US
dc.publisherAIP Publishing
dc.titleSurface Waves in Closed Basins under Parametric And Internal Resonancesen_US
dc.typeArticleen_US
dc.identifier.urlhttp://scitation.aip.org/content/aip/journal/pof1/30/10/10.1063/1.866075
dc.date.accessed2014-04-04
dc.title.serialPhysics of Fluids
dc.identifier.doihttps://doi.org/10.1063/1.866075
dc.type.dcmitypeTexten_US


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