Nonlinear wave propagation, acoustic

Nonlinear Wave Propagation. It is assumed that most acoustic measurements are made in the linear wave propagation region, ie, where Hooke s law applies. Polymers as a class, however, are more nonlinear than other solids. Nonlinear wave propagation is therefore significant in some cases. 

Because of the high amplitudes of particle motion in the fluid due to (1) and (2), nonlinear acoustic effects can be important. In particular, acoustic streaming can occur, so that a propagating sinusoidal wave produces a steady ( zero frequency ) force in the direction of wave propagation. This steady force causes fluids in contact with the membrane to move. 

Ultrasonic transducers can excite various wave modes, eg, guided Lamb waves that may be suitable for specific apphcations (143). Ultrasonic excitation is also used to detect the so-called acoustic nonlinearity associated with defects, eg, in PMC (144,145). The combination of recording guided ultrasonic waves with numerical back-calculation of wave propagation for detecting indications of defects in PMC pipes also looks promising (146). Surface-bonded fiber optics can detect ultrasonic waves via interferometric techniques (147). Beyond frequencies of 1 GHz, ultrasonics is called acoustic microscopy, for details, the reader is referred to Reference 148. This technique can be applied to polymers or PMC (149), specifically to polymeric microelectronics packaging (150). 

Nonlinear phenomena, usually associated with high amplitudes of the acoustic field, can introduce many interesting effects into acoustic instability [76]. Here we shall discuss only three topics involving nonlinearity the response of the combustion zone to transverse velocity oscillations (conventionally termed velocity coupling), changes in the mean burning rate of the propellant in the presence of an acoustic field, and instabilities that involve the propagation of steep-fronted waves (identified in the introduction as shock instabilities). 

Many of the phenomena in acoustics can be described by means of a theory either linear in acoustic amplitude or including the first term of non-linear equations. In sonochemistry, the displacement amplitude of the wave is so large that nonlinear terms of the propagation equation cannot be neglected. 546 This leads to considerable complexity in the description. In this section, we follow a route of increasing complexity up to the major question what can be done to quantify the medium in which sonochemistry (or sonoluminescence) occurs ... 

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