### ASA 129th Meeting - Washington, DC - 1995 May 30 .. Jun 06

## 3aPA9. Numerical anomalies in the Rayleigh--Ritz method for calculating
the normal mode vibrations of arbitrarily shaped elastic solids.

**P. S. Spoor
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J. D. Maynard
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*Dept. of Phys., Penn State Univ., University Park, PA 16802
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A matrix implementation of the Rayleigh--Ritz variational method was used
by Demarest [H. H. Demarest, 768] to make the first successful
calculation of the eigenfrequencies and eigenmodes of an isotropic elastic
cube, and was later generalized by Ohno [I. Ohno, J. Phys. Earth 57, 355] and
Visscher [W. M. Visscher et al., 2154--2162 (1991)] to apply to solids
of arbitrary shape and elastic symmetry. This became the core of a new method
of elastic constant determination based on measurements of the normal mode
spectra of elastic parallelepipeds and spheres, called resonant ultrasound
spectroscopy (RUS). In theory, one should be able to use Rayleigh--Ritz to
determine the effect of imperfect parallelepipeds (due to small errors in
sample preparation) on the accuracy of RUS. It has been discovered, however,
that the method may not converge properly for many relevant cases, producing
spurious results. A variety of examples, including comparisons with low-order
approximations, will be discussed. [Work supported by NSF Grant DMR-9000549 and
by the Office of Naval Research.]