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

J. D. Maynard

Dept. of Phys., Penn State Univ., University Park, PA 16802

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.]