Engineering Transactions, 41, 1, pp. 97-116, 1993

Diffraction of Torsional Elastic Waves by a Rigid Annular Disc at a Bimaterial Interface

S.C. Mandal
North Bengal University, Darjeeling
India

M.L. Gosh
North Bengal University, Darjeeling
India

The problem of diffraction of normally incident torsional wave by an annular rigid disc lying at the interface of two bonded dissimilar semi-infinite elastic media is analysed. The three-part mixed boundary value problem is reduced to the solution of a set of integral equations which are solved by using iterative technique for low frequency, assuming that the ratio of the inner and outer radii is small. The stress distribution on the disc, the torque and far-field amplitudes of the displacement in both the media are evaluated. The variation of dynamic stress intensity factors with normalised frequency for various values of the material parameters, and also the variation in far-field amplitude with the polar angles for a fixed radial distance have been shown by means of graphs.

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References

Y.ONDER, E.S.SUHUBI and M.IDEMEN, Diffraction of scalar elastic waves by a rigid half-plane between two semi-infinite media, Lett. Appl. Engng. Sci., 3, 15-24, 1975.

A.K.MAL, Interaction of elastic waves with a Griffith crack, Int. J. Engng. Sci., 8, 763, 1970.

K.N.SRIVASTAVA, R.M.PALAIYA and D.S.KARAULIA, Interaction of antiplane shear waves by a Griffith crack at the interface of two bonded dissimilar elastic half-spaces, Int. J. Fract., 16, 349-3581 1980.

A.BOSTROM, Elastic wave scattering from an interface crack. Antiplane strain, J. Appl. Mech., 54, 503-508, 1987.

S.KRENK and H.SCHMIDT, Elastic wave scattering by a circular crack, Phil. Trans. R. Soc. Lond., A308, 167-198, 1982.

R.M.PALAIYA and P.MAJUMDER, lnteraction of antiplane shear waves by rigid strip lying at the interface of two bonded dissimilar elastic half-spaces, ZAMM, 61, 120-122, 1981.

S.UEDA, Y.SHINDO and A.ATSUMI, Torsional impact response of a penny-shaped crack lying on a bimaterial interface, Engng. Fract. Mech., 18, 1059-1066, 1983.

Y.SHINDO, Diffraction of torsional waves by a flat annular crack in an infinite elastic medium, J. Appl. Mech., 46, 827-831, 1979.

Y.SHINDO, Sudden twisting of a flat annular crack, Int. J. Solids Structure, 17, 1103-1112, 1981.

F.ERDOGAN, Stress distribution in bonded dissimilar materials containing circular or ring-shaped cavities, ASME J. Appl. Mech., 32, 829-836, 1965.

F.ERDOGAN, Approximate solutions of system of singular integral equations, SIAM J. Appl. Mech., 17, 1041-1059, 1969.

D.P.THOMAS, Acoustic diffraction by an annular disc, Int. J. Engng. Sci., 3, 405-416, 1965.

W.E.WILLIAMS, Integral equation formulation of some three-part boundary value problems, Proc. Edinb. Math. Soc., II, 13, 317-323, 1963.

D.L.JAIN and R.P.KANWAL, Torsional oscillations of an elastic half-space due to an annular disc and related problems, Int. J. Engng. Sci., 8, 687-698, 1970.

R.P.KANWAL, Linear integral equations-theory and technique, Academic Press, London 1971.

S.C.MANDAL and M.L.GHOSH, Forced vertical vibration of two rigid strips on a semi-infinite elastic solid, J. Sound and Vibration, 158(1), 169-179, 1992.




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