### ASA 130th Meeting - St. Louis, MO - 1995 Nov 27 .. Dec 01

## 2aPA4. Nonlinear acoustics of rocks and other hard subjects.

**M. A. Breazeale
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*Natl. Ctr. for Physical Acoustics, University of Mississippi, University,
MS 38677
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With single crystals, an acceptable approximation is achieved with only the
first nonlinear term in the wave equation. With such crystals and weakly
nonlinear solids, one can define a nonlinearity parameter (beta) as the negative
ratio of the coefficients of the nonlinear and the linear terms. Values of
(beta) between three and 15 have been observed for single crystals. It appears
that the approximation no longer is adequate when (beta) becomes larger. Values
of (beta) between 80 and 1000 have been observed for rocks. A value of
(beta)=1500 has been observed for PZT at the Curie temperature. In addition,
frequency dispersion of the nonlinearity has been observed in PZT, and the third
harmonic is much larger than expected from an extrapolation of second harmonic
data. Since the approximate theory no longer is adequate, terms have been added
to the nonlinear equation. The nonlinear equation required to fit data on PZT
has been determined. The next step is to explain this mathematical success in
physical terms. This will involve the effect of grain boundaries. Then the
results can be applied to rocks, which are more complicated.