R. E. Kumon, ``Nonlinear surface acoustic waves in cubic crystals,'' Ph. D. dissertation, The University of Texas at Austin (1999).

Model equations developed by Hamilton, Il'inskii, and Zabolotskaya
[*J. Acoust. Soc. Am.* **105**, 639-651 (1999)] are employed
to perform theoretical and numerical studies of nonlinear
surface acoustic waves in a variety of nonpiezoelectric cubic
crystals. The basic theory underlying the model equations
is outlined, quasilinear solutions of the equations
are derived, and expressions are developed
for the shock formation distance and nonlinearity
coefficient. A time-domain equation corresponding to the
frequency-domain model equations is derived and shown to reduce
to a time-domain equation introduced previously for Rayleigh waves
[E. A. Zabolotskaya, *J. Acoust. Soc. Am.* **91**,
2569-2575 (1992)]. Numerical calculations are performed
to predict the evolution of initially monofrequency surface waves in
the (001), (110), and (111) planes of the crystals
RbCl, KCl, NaCl, CaF_{2}, SrF_{2}, BaF_{2}, C (diamond),
Si, Ge, Al, Ni, Cu in the *m*[`3]*m* point group and the crystals
Cs-alum, NH_{4}-alum, and K-alum in the *m*[`3] point group.
The calculations are based on
measured second- and third-order elastic constants taken
from the literature. Nonlinearity matrix elements which describe
the coupling strength of harmonic interactions are shown to
provide a powerful tool for characterizing waveform distortion.
In the (001) and (110) planes, the simulations show
that in certain directions the velocity waveform distortion
may change in sign, generation of one or more harmonics
may be suppressed and shock formation postponed, or energy
may be transferred rapidly to the highest harmonics
and shock formation enhanced. Simulations in the (111)
plane show that the nonlinearity matrix elements are
generally complex-valued, which may lead to asymmetric
distortion and the appearance of low frequency oscillations near the
peaks and shocks in the velocity waveforms.
A simple transformation based on the phase of the
nonlinearity matrix elements is shown to
provide a reasonable approximation of asymmetric
waveform distortion in many cases.
Finally, numerical simulations are corroborated by measured
pulse data from an external collaboration with
P. Hess, A. Lomonosov, and V. G. Mikhalevich.
Pulsed waveforms in the (001) and (111) planes of crystalline silicon
are quantitatively reproduced, and two distinct regions of
nonlinear distortion are confirmed to exist in the (001) plane.

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Ronald Kumon / Acoustics Group / UT Austin / Created 30 Oct 1999 / Updated 30 Oct 1999