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The Quarterly Journal of Mechanics and Applied Mathematics 1994 47(4):583-606; doi:10.1093/qjmam/47.4.583
© 1994 by Oxford University Press
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TRANSMISSION AND REFLECTION OF ELASTIC WAVES BY A SPHERICAL OBSTACLE IN AN INFINITE CIRCULAR CYLINDRICAL ROD

SUNE OLSSON

( Division of Mechanics, Chalmers University of Technology S-41296 Göteborg, Sweden )

The null-field approach is applied to the problem of scattering of elastic waves by a spherical obstacle in an infinite circular cylindrical rod. The axially symmetric longitudinal and vertically polarized, transverse waves are considered and the boundary conditions are those of vanishing surface traction. Thus the scattered field is obtained as a complicated mode sum containing the transition matrix of the sphere, the reflection matrix of the cylinder and the transformation function between the spherical and cylindrical vector wave functions. The transmission and reflection coefficients are extracted and energy conservation is utilized as a check on the numerical procedure. Finally, numerical results showing the energy transmission and reflection coefficients as functions of both frequency and sphere radius are presented.


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