Title page for ETD etd-081999-174631


Type of Document Master's Thesis
Author Andrews, Mary Frances
URN etd-081999-174631
Title Evolution Equations for Weakly Nonlinear, Quasi-Planar Waves in Isotropic Dielectrics and Elastomers
Degree Master of Science
Department Engineering Mechanics
Advisory Committee
Advisor Name Title
Cramer, Mark S. Committee Chair
Hendricks, Scott L. Committee Member
Henneke, Edmund G. II Committee Member
Keywords
  • nonlinear wave propagation
  • nonlinear dielectrics
  • hyperelastic solids
  • Zabolotskaya-Khokhlov
Date of Defense 1999-08-19
Availability unrestricted
Abstract
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.
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