On the normal modes of free vibration of inhomogeneous and anisotropic elastic objects

Journal of the Acoustical Society of America

Volumn 90, Issue 4, 1991, Pages 2154-2162

  Visscher, William M ^a   Mialiori, Albert ^a   Bell, Thomas M ^a   Reinert, Robert A ^a  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACOUSTICS; ARTICLE;

EID: 0025932079     PISSN: 00014966     EISSN: NA     Source Type: Journal    
DOI: 10.1121/1.401643     Document Type: Article

References (20)

1. R. Holland, J. Acoust. Soc. Am. 43, 988 (1968).
2. H. H. Demarest, Jr., Bachelor’ thesis, Reed College, Portland, OR (1969).
3. H. H. Demarest, Jr., J. Acoust. Soc. Am. 49, 768 (1971).
4. I. Ohno, J. Phys. Earth 24, 355 (1976).
5. Y. Sumino, I. Ohno, T. Goto, and M. Kumazawa, J. Phys. Earth 24, 263 (1976).
6. I. Ohno, S. Yamamoto, O. L. Anderson, and J. Noda, J. Phys. Chem. Solids 47, 1103 (1986).
7. A. Migliori, W. M. Visscher, S. E. Brown, Z. Fisk, S.-W. Cheong, B. Al-ten, E. T. Ahrens, K. A. Kubat-Martin, J. D. Maynard, Y. Huang, D. R. Kirk, K. A. Gillis, H. K. Kim, and M. H. W. Chan. Phys. Rev. B 41, 2098 (1990).
8. A. Migliori, W. M. Visscher, S. Wong, S. E. Brown, I. Tanaka, H. Kojima, and P. B. Allen. Phys. Rev. Lett. 64, 2408 (1990).
9. E. Mochizuki, J. Appl. Phys. 63, 5668 (1988).
10. S. Isoda, H. Oda, I. Suzuki, and K. Seya, Tohoku Geophys J. 32, 55 (1990).
11. See the famous paper, “Can One Hear the Shape of a Drum?” by M. Kac, Am. Math. Month. 73, 1 (1966).
12. For more recent work, see M. H. Prot-ter, SIAM Rev. 29, 185 (1987).
13. A. Stekel, J. L. Sarrao, T. M. Bell, Ming Lei, R. G. Leisure, W. M. Visscher, and A. Migliori (to be published).
14. B. T. Smith, J. M. Boyle, J. J. Dongarra, B. S. Garbow, Y. Ikebe, V. C. Klema, and C. B. Moler, “Matrix Eigensystem Routines—EISPACK Guide,” in Lecture Notes in Computer Science No. 6, edited by G. Goos and J. Hartmanis (Springer, New York, 1976).
15. B. S. Garbow, J. M. Boyle, J. J. Dongarra, and C. B. Moler, “Matrix Eigensystem Routines—EISPACK Guide Extension,” in Lecture Notes in Computer Science No. 51, edited by G. Goos and J. Hartmanis (Spring-er, New York, 1977).
16. Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun (National Bureau of Standards Applied Mathematics Series No. 55, Washington, DC, 1965), p. 258.
17. M. Marcus, Basic Theorems in Matrix Theory (National Bureau of Standards Applied Mathematics Series No. 57, Washington, DC, 1960), p. 12.
18. F. Birch, J. Geophys. Res. 80, 756 (1974). This paper, concerned with vibrations of steel, glass, and rock spheres, provides a precedent for comparing measured and computed normal-mode frequencies of objects with simple geometries.
19. L. D. Landau, E. M. Lifshitz, A. M. Kosevich, and L. P. Pitaevskii, Theo-rv of Elasticity (Pergamon. New York, 1986).
20. H. Lamb, Proc. Math Soc. 13, 189 (1882).