### ASA 128th Meeting - Austin, Texas - 1994 Nov 28 .. Dec 02

## 4pPAa10. Extensions of the theory for nonlinear Rayleigh waves.

**E. Yu. Knight
**

**
M. F. Hamilton
**

**
Yu. A. Il
**

**
E. A. Zabolotskaya
**

**
**
*Dept. of Mech. Eng., Univ. of Texas at Austin, Austin, TX 78712-1063
*

*
*
The derivation of Zabolotskaya's coupled spectral equations for nonlinear
Rayleigh waves in isotropic solids [J. Acoust. Soc. Am. 91, 2569 (1992)]
applies to plane, progressive, periodic waves. These assumptions are removed
here in a more general derivation based on the Hamiltonian formalism employed
in the original work. Via methods described in Paper 4pPAa12 of this session,
the resulting spectral equations are transformed into time domain evolution
equations. Model equations for cylindrical waves and diffracting beams,
obtained previously via ad hoc modification of the plane-wave model, can be
derived rigorously from the new generalized equations. The nonlinear terms are
shown to be equivalent to those obtained previously by Parker [Int. J. Eng.
Sci. 26, 113 (1985)] by entirely different methods. Numerical results for the
shock formation distance are used to define an effective coefficient of
nonlinearity that is consistent with the corresponding parameter for sound
waves in fluids. The coefficient is of order one for common isotropic solids,
as for the case of fluids, but it is several orders of magnitude larger in rock
with microcracks and other inhomogeneous features. [Work supported by DOE, ONR,
and NSF.]