Evolution Equations for Weakly Nonlinear, Quasi-Planar Waves in Isotropic Dielectrics and Elastomers

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dc.contributor.authorAndrews, Mary F.en
dc.contributor.committeechairCramer, Mark S.en
dc.contributor.committeememberHenneke, Edmund G. IIen
dc.contributor.committeememberHendricks, Scott L.en
dc.contributor.departmentEngineering Mechanicsen
dc.date.accessioned2014-03-14T20:43:48Zen
dc.date.adate1999-09-18en
dc.date.available2014-03-14T20:43:48Zen
dc.date.issued1999-08-19en
dc.date.rdate2000-09-18en
dc.date.sdate1999-08-19en
dc.description.abstractThe propagation of waves through nonlinear media is of interest here, namely as it pertains to two specific examples, a nonlinear dielectric and a hyperelastic solid. In both cases, we examine the propagation of two-dimensional, weakly nonlinear, quasi-planar waves. It is found that such systems will have a nonlinearity that is intrinsically cubic, and therefore, a classical Zabolotskaya-Khokhlov equation cannot give an accurate description of the wave evolution. To determine the general evolution equation in such systems, a multi-timing technique developed by Kluwick and Cox (1998) and Cramer and Webb (1998) will be employed. The resultant evolution equations are seen to involve only one new nonlinearity coefficient rather than the three coefficients found in other studies of cubically nonlinear systems. After determining the general evolution equation, inclusion of relaxation, dispersion and dissipation effects can be easily incorporated.en
dc.description.degreeMaster of Scienceen
dc.identifier.otheretd-081999-174631en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-081999-174631/en
dc.identifier.urihttp://hdl.handle.net/10919/34649en
dc.publisherVirginia Techen
dc.relation.haspart1MARYANDREWS.PDFen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectnonlinear wave propagationen
dc.subjectnonlinear dielectricsen
dc.subjecthyperelastic solidsen
dc.subjectZabolotskaya-Khokhloven
dc.titleEvolution Equations for Weakly Nonlinear, Quasi-Planar Waves in Isotropic Dielectrics and Elastomersen
dc.typeThesisen
thesis.degree.disciplineEngineering Mechanicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.levelmastersen
thesis.degree.nameMaster of Scienceen

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