| 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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| Files |
| Filename |
Size |
Approximate Download Time
(Hours:Minutes:Seconds)
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| 28.8 Modem |
56K Modem |
ISDN (64 Kb) |
ISDN (128 Kb) |
Higher-speed Access |
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1MARYANDREWS.PDF |
361.70 Kb |
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