a Dissipative Wave Packet Approach for Unified Nonlinear Acoustics
Abstract
Nonlinear acoustic waves are investigated from the viewpoint of a wavepacket. The wavepacket is defined as a portion of a wave that travels at an independent phase speed c = c_{o} + beta u ^', where c_{o } is the sound speed, beta is a constant related to the propagation nonlinearity, and u^' is the acoustic particle velocity. During travel the wave distorts because of the nonlinearity, and undergoes absorption due to the effects of viscosity, heat conduction, and relaxation. Some of the most interesting phenomena associated with nonlinear acoustic waves are the result of the combined effects of nonlinear propagation (and the resulting distortion of the wave) and of absorption. These effects are especially at work in shock problems. The mathematical approach begins with the notion of cumulative wave distortion, and its development from a nonlinear wave equation. Novel time domain expressions for acoustic absorption are then developed which are valid for both linear and nonlinear acoustic waves. These theoretical concepts, for nonlinear propagation and for absorption, are then combined into a propagation model which is then evaluated numerically in the spatial domain. Several specific and diverse examples are emphasized, including: pulse self demodulation, oceanic parametric sonar, enhancement of ultrasound heating by soundsound nonlinear interaction, and the formation and evolution of acoustic shocks without the need for the socalled equalarea rule in weak shock theory. Experimental data are used to verify both the theory and the computational results. (Copies available exclusively from MIT Libraries, Rm. 140551, Cambridge, MA 021394307. Ph. 6172535668; Fax 6172531690.).
 Publication:

Ph.D. Thesis
 Pub Date:
 1994
 Bibcode:
 1994PhDT........43R
 Keywords:

 ACOUSTICS;
 Physics: Acoustics; Applied Mechanics