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

The 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.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Engineering Mechanics

Department dc:contributor.department

Engineering Mechanics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

1999

Author dc:creator

• Andrews, Mary F.

Chair dc:contributor.committeechair

• Cramer, Mark S.

Committee members dc:contributor.committeemember

• Henneke, Edmund G. II
• Hendricks, Scott L.

• nonlinear wave propagation
• nonlinear dielectrics
• hyperelastic solids
• Zabolotskaya-Khokhlov

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-081999-174631

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/34649