Toroidal vibrations of anisotropic spheres with spherical isotropy

Journal of Applied Mechanics, Transactions ASME

Volumn 65, Issue 1, 1998, Pages 59-65

  Chau, K T ^a  

^a HONG KONG POLYTECHNIC UNIVERSITY   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002531080     PISSN: 00218936     EISSN: 15289036     Source Type: Journal    
DOI: 10.1115/1.2789046     Document Type: Article

References (44)

1. Abramowitz, M., and Stegun, I. A., 1965, Handbook of Mathematical Functions, Dover, New York.
2. Alsop, L. E., Sutton, G. H., and Ewing, M., 1961, “Free oscillations of the Earth observed on strain and pendulum seismographs,” Journal of Geophysical Research, Vol. 66, pp. 631-641.
3. Benioff, H., Press, F., and Smith, S., 1961, “Excitation of the free oscillations of the Earth by earthquakes,” Journal of Geophysical Research, Vol. 66, pp. 605-619.
4. Bogert, B. P., 1961, “An observation of free oscillations of the Earth,” Journal of Geophysical Research, Vol. 66, pp. 643-646.
5. Chau, K. T., 1993, “Natural frequencies of finite transversely isotropic circular cylinders,” Proceedings of the Second International Conference on Vibration Problems of Mathematical Elasticity and Physics, M. M. Banerjee and P. Biswas, eds., Vol. A, pp. 7-12.
6. Chau, K. T., 1994, “Vibrations of transversely isotropic finite circular cylinders,” ASME Journal of Applied Mechanics, Vol. 61, pp. 964-970.
7. Chau, K. T., 1995, “Bifurcations at a spherical cavity in a compressible solid with spherical isotropy,” International Journal for Numerical and Analytical Methods in Geo mechanics, Vol. 19, pp. 381-398.
8. Chen, W. T., 1966, “On some problems in spherically isotropic elastic materials,” ASME Journal of Applied Mechanics, Vol. 33, pp. 539-546.
9. Chree, C., 1889, “The equations of an isotropic elastic solid in polar and cylindrical coordinates, their solution and application,” Transactions of Cambridge Philosophical Society, Vol. 14, pp. 250-369.
10. Ding, H.-J., and Ren, Y.-J., 1991, “Equilibrium problems of spherically isotropic bodies,” Applied Mathematics and Mechanics, Vol. 12, pp. 155-162 (English Ed.).
11. Eason, G., 1962, “On the vibrations of anisotropic cylinders and spheres,” Applied Scientific Research, Vol. A12, pp. 81-85.
12. Eason, G., 1963, “Transient thermal stresses in anisotropic bodies with spherical symmetry,” Applied Scientific Research, Vol. A13, pp. 1-15.
13. Fraser, D. B., and LeCraw R. C., 1964, “Novel method of measuring elastic and anelastic properties of solids,” The Review of Scientific Instruments, Vol. 35, pp. 1113-1115.
14. Hata, T., 1993, “Stress-focusing effect in a uniformly heated transversely isotropic sphere,” International of Journal of Solids and Structures, Vol. 30, pp. 1419-1428.
15. Hearmon, R. F. S., 1969, “The elastic constants of non-piezoelectric crystals,” Numerical Data and Functional relationships in Science and Technology, New Series, group 3, H. H. Landolt and R. Bomstein ed., Vol. 1, pp. 1-39.
16. Heyliger, P., Ledbetter, H., and Austin, M., 1990, “Resonating-orthotropic-cube method for elastic constants,” Dynamics Elastic Modulus Measurements in Materials, ASTM STP 1045, ASTM, Philadelphia, PA, pp. 100-109.
17. Heyliger, P. R., and Jilani, A., 1991, “The free vibrations of elastic anisotropic cylinders and spheres,” 32nd Structures, Structural Dynamics, and Materials Conference, AIAA, Part 4, Structural Dynamics II, pp. 3039-3046.
18. Heyliger, P. R., and Jilani, A., 1992, “The free vibrations of inhomogeneous elastic cylinders and spheres,” International Journal of Solids and Structures, Vol. 29, pp. 2689-2708.
19. Hobson, E. W., 1955, The Theory of Spherical and Ellipsoidal Harmonics, Chelsea Publishing Company, New York.
20. Hosseini-Hashemi, S., and Anderson, J. S., 1988, “Orthogonality and normalization of torsional modes of vibration of solid elastic spheres,” Journal of Sound and Vibration, Vol. 121, pp. 511-524.
21. Hu, H.-C., 1954, “On the general theory of elasticity for a spherically isotropic medium,” Acta Scientia Sinica, Vol. 3, pp. 247-260.
22. Isoda, S., Oda, H., Suzuki, I., and Seya, K., 1990, “Displacement distribution of a freely oscillating rutile sphere,” Tohoku Geophysical Journal, Vol. 32, pp. 55-76.
23. Kelvin, Lord, 1863, “On the rigidity of the Earth,” Philosophical Transactions of the Royal Society of London, Vol. A153, pp. 573-582.
24. Lamb, H., 1882, “On the vibrations of a elastic sphere,” Proceedings of the London Mathematical Society, Vol. 13, pp. 189-212.
25. Lapwood, E. R., and Usami, T., 1981, Free Oscillations of the Earth, Cambridge University Press, Cambridge, UK.
26. Love, A. E. H., 1944, A Treatise on the Mathematical Theory of Elasticity, Dover, New York.
27. MacDonald, G. J. F., and Ness, N. F., 1961, “A study of the free oscillations of the Earth,” Journal of Geophysical Research, Vol. 66, pp. 1865-1911.
28. Malvern, L. E., 1969, Introduction to the Mechanics of a Continuous Medium, Prentice-Hall, Englewood Cliffs, NJ.
29. Mochizuki, E., 1986, “The free oscillation of an anisotropic and heterogeneous earth,” Geophysical Journal of Royal Astro nautical Society, Vol. 86, pp. 167-176.
30. Mochizuki, E., 1988, “Sphere-resonance method to determine elastic constants of crystal,” Journal of Applied Physics, Vol. 63, pp. 5668-5673.
31. Nemish, Yu. N., 1969, “Approximate solution of three-dimensional problems in elasticity theory for a transversely isotropic medium,” Soviet Applied Mechanics, Vol. 5, pp. 803-810.
32. Nemish, Yu. N., and Nemish, V. N., 1976, “Contribution of the solution of spatial problems of the elasticity theory of a transversely isotropic medium for noncanonical regions,” Soviet Applied Mechanics, Vol. 12, pp. 1262-1270.
33. Ness, N. F., Harrison, J. C., and Slichter, L. B., 1961, “Observations of the free oscillations of the Earth,” Journal of Geophysical Research, Vol. 66, pp. 621-629.
34. Nowinski, J., 1959, “Note on a thermo elastic problem for a transversely isotropic hollow sphere embedded in an elastic medium,” ASME Journal of Applied Mechanics, Vol. 26, pp. 649-650.
35. Payton, R. G., 1983, Elastic Wave Propagation in Transversely Isotropic Media, Martinus Nijhoff, Hague.
36. Perkeris, C. L., Alterman, Z., and Jarosch, H., 1961, “Comparison of theoretical with observed values of the periods of free oscillation of the Earth,” Proceedings of the National Academy of Science, Vol. 47, pp. 91-98.
37. Press, W. H., Teukolsky, S. A., Vetterling, W. T. and Flannery, B. P., 1992, Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed., Cambridge University Press, Cambridge, UK.
38. Puro, A. E., 1980, “Variable separation in elasticity-theory equations for spherically transversely isotropic inhomogeneous bodies,” Soviet Applied Mechanics, Vol. 16, pp. 117-121.
39. Sato, Y., and Usami, T., 1962a, “Basic study on the oscillation of a homogeneous elastic sphere: I. Frequency of the free oscillations,” Geophysical Magazine, Vol. 31, pp. 15-24.
40. Sato, Y., and Usami, T., 1962b, “Basic study on the oscillation of a homogeneous elastic sphere: II. Distribution of displacement,” Geophysical Magazine, Vol. 31, pp. 25-47.
41. Shreiber, E., Anderson, O. L., and Soga, N., 1973, Elastic Constants and Their Measurement, McGraw-Hill, New York.
42. Sur, S. P., 1964, “Vibration of inhomogeneous spherical shell of aeolotropic materials,” Indian Journal of Mechanics and Mathematics, Vol. 2, pp. 6-9.
43. Visser, W. M., Migliori, A., Bell, T. M., and Reinert, R. A., 1991, “On the normal modes of free vibration of inhomogeneous and anisotropic elastic objects,” Journal of the Acoustical Society of America, Vol. 90, pp. 2154-2162.
44. Whittaker, E. T., and Watson, G. N., 1927, A Course of Modern Analysis, 4th Ed. Cambridge University Press, Cambridge, UK.