Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 31103
Analytical Solution of Time-Harmonic Torsional Vibration of a Cylindrical Cavity in a Half-Space

Authors: M.Eskandari-Ghadi, M.Mahmoodian


In this article an isotropic linear elastic half-space with a cylindrical cavity of finite length is considered to be under the effect of a ring shape time-harmonic torsion force applied at an arbitrary depth on the surface of the cavity. The equation of equilibrium has been written in a cylindrical coordinate system. By means of Fourier cosine integral transform, the non-zero displacement component is obtained in the transformed domain. With the aid of the inversion theorem of the Fourier cosine integral transform, the displacement is obtained in the real domain. With the aid of boundary conditions, the involved boundary value problem for the fundamental solution is reduced to a generalized Cauchy singular integral equation. Integral representation of the stress and displacement are obtained, and it is shown that their degenerated form to the static problem coincides with existing solutions in the literature.

Keywords: torsion, isotropic, Cosine transform, Half space, Singular integral equation

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1268


[1] H. M. Westergaard, Theodore von karman Anniversary Volume, 154- 161, Caltech, 1941.
[2] D. W. Jordan, "The stress wave from a finite cylindrical explosive source", J. Math. Mech. 11, 503-551, 1962.
[3] R. P. Srivastava, "A axisymetric mixed boundary value problem for a half space with a cylindrical cavity", J. Math. Mech. 13, 385-393, 1964.
[4] R. P. Srivastava, and P. Narain, "Stress distribution due to pressurized exterior crack in an infinite isotropic elastic medium with coaxial cylindrical cavity", Int. J. Engng. Sci. 4, 689-697, 1966.
[5] R. Parnes, "Applied tractions on the surface of an infinite cylindrical bore", Int. J. Solids Structures 19, 165-177, 1982.
[6] R. Parnes, "Elastic response to a time-harmonic torsion-force acting on a bore surface", Int. J. Solids Structures 19, 925-934, 1983.
[7] R. Y. S. Pak, and F. Abedzadeh, "Torsional traction on an open finite cylindrical cavity", Proc. R. Soc. Lond. A 438, 133-144, 1992.
[8] S. G. Lekhnitskii, "Theory of elasticity of an anisotropic body", Mir Publisher Moscow, 1981.
[9] I. N. Sneddon, "Fourier Transforms", 1st ed., New York, McGraw-Hill, 1951.
[10] N. I. Muskhelishvil, "Singular integral equations", 1st Edn. P. Noordhoff, Groningen, 1953.
[11] F. Erdogan, "Mixed boundary value problems in mechanics", Mech. Today 4, 1-86, 1979.
[12] L.C. Andrews, "Special functions of mathematics for engineers", 2nd Edn. Oxford University press, 1998.