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TECHNICAL PAPERS

Transient Response of an Infinite Elastic Medium Containing a Spherical Cavity Subjected to Torsion

[+] Author and Article Information
U. Zakout

Department of Civil Engineering, Middle East Technical University, 0s6531 Ankara, Turkey

Z. Akkas

Department of Engineering Sciences, Middle East Technical University, 0s6531 Ankara, Turkey

G. E. Tupholme

School of Computing and Mathematics, University of Bradford, Bradford, West Yorkshire BD7 1DP, UK

J. Appl. Mech 67(2), 282-287 (Dec 07, 1999) (6 pages) doi:10.1115/1.1303985 History: Received November 20, 1998; Revised December 07, 1999
Copyright © 2000 by ASME
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References

Achenbach, J. D., 1972, Wave Propagation in Elastic Solids, North-Holland, Amsterdam.
Eringen, A. C., and Suhubi, E. S., 1974–1975, Elastodynamics, Vols. 1 and 2, Academic Press, New York.
Miklowitz, J., 1978, The Theory of Elastic Waves and Waveguides, North-Holland, Amsterdam.
Gaunaurd,  G. C., 1989, “Elastic and Acoustic Resonance Wave Scattering,” Appl. Mech. Rev., 42, pp. 143–193.
Sato,  Y., Usami,  T., and Ewing,  M., 1962, “Basic Study on the Oscillation of a Homogeneous Elastic Sphere, Part IV—Propagation of Disturbances on the Sphere,” Geophysics, 31, pp. 237–241.
Godin,  Y. A., 1995, “An Exact Solution to a Problem of Axisymmetric Torsion of an Elastic Space With a Spherical Crack,” Q. Appl. Math., LIII, pp. 679–682.
Chadwick,  P., and Trowbridge,  E. A., 1967, “Oscillations of a Rigid Sphere Embedded in an Infinite Elastic Solid, Part I—Torsional Oscillations,” Proc. Cambridge Philos. Soc., 63, pp. 1189–1205.
Chadwick,  P., and Trowbridge,  E. A., 1967, “Oscillations of a Rigid Sphere Embedded in an Infinite Elastic Solid, Part II—Rectilinear Oscillations,” Proc. Cambridge Philos. Soc., 63, pp. 1207–1227.
Chadwick,  P., and Trowbridge,  E. A., 1967, “Elastic Wave Fields Generated by Scalar Wave Functions,” Proc. Cambridge Philos. Soc., 63, pp. 1177–1187.
Tupholme,  G. E., 1983, “Elastic Pulse Generation by Tractions Applied to a Spherical Cavity,” Appl. Sci. Res., 40, pp. 299–325.
Tupholme,  G. E., 1967, “Generation of an Axisymmetrical Acoustic Pulse by a Deformable Sphere,” Proc. Cambridge Philos. Soc., 63, pp. 1285–1308.
Chadwick,  P., and Johnson,  A. F., 1969, “Torsional Oscillations of a Rigid Convex Inclusion Embedded in an Elastic Solid,” J. Inst. Math. Appl., 5, pp. 283–307.
Geers,  T. L., 1969, “Excitation of an Elastic Cylindrical Shell by a Transient Acoustic Wave,” ASME J. Appl. Mech., 36, pp. 459–469.
Akkas,  N., 1979, “Residual Potential Method in Spherical Coordinates and Related Approximations,” Mech. Res. Commun., 6, pp. 257–262.
Akkas,  N., 1985, “The Residual Variable Method and its Applications,” Acta Mech., 55, pp. 203–217.
Akkas,  N., and Zakout,  U., 1997, “Transient Response of an Infinite Elastic Medium Containing a Spherical Cavity With and Without a Shell Embedment,” Int. J. Eng. Sci., 35, pp. 89–112.
Zakout,  U., and Akkas,  N., 1997, “Transient Response of a Cylindrical Cavity With and Without a Bonded Shell in an Infinite Elastic Medium,” Int. J. Eng. Sci., 35, pp. 1203–1220.
Abramowitz, M., and Stegun, I. A., eds., 1965, Handbook of Mathematical Functions, Dover, New York.

Figures

Grahic Jump Location
Geometry of the problem
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Circumferential stresses for n=1 at various values of r
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Circumferential stresses for n=2 at various values of r
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Circumferential stresses for n=3 at various values of r
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Circumferential stresses for n=1 to 14 at r=1.1
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Circumferential stresses for n=1 to 14 at r=1.2
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Circumferential displacements for n=1 at various values of r
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Circumferential displacements for n=1 to 14 at r=1.0
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Circumferential stresses for n=1 at various values of t
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Torsional stresses for n=1 to 12 and n=1 to 14 in Load Case 1 at r=1.1, 1.2 and 1.5 with θ=π/2
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Torsional stresses for n=1 to 12 and n=1 to 14 in Load Case 1 at r=1.1, 1.2 and 1.5 with θ=π/4
Grahic Jump Location
Torsional stresses for n=1 to 12 and n=1 to 14 in Load Case 2 at r=1.2 and 1.5 with θ=π/2
Grahic Jump Location
Torsional stresses for n=1 to 12 and n=1 to 14 in Load Case 2 at r=1.2 and 1.5 with θ=π/4

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