International Journal of Mathematics and Mathematical Sciences
Volume 4 (1981), Issue 2, Pages 393-405

On elastic waves in a medium with randomly distributed cylinders

S. K. Bose1 and L. Debnath2

1Department of Mathematics, Regional Engineering College, Durgapur 713209, India
2Mathematics Department, East Carolina University, Greenville 27834, North Carolina, USA

Received 12 August 1980

Copyright © 1981 S. K. Bose and L. Debnath. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A study is made of the problem of propagation of elastic waves in a medium with a random distribution of cylinders of another material. Neglecting ‘back scattering’, the scattered field is expanded in a series of ‘orders of scattering’. With a further assumption that the n(n>2) point correlation function of the positions of the cylinders could be factored into two point correlation functions, the average field in the composite medium is found to be resummable, yielding the average velocity of propagation and damping due to scattering. The calculations are presented to the order of (ka)2 for the scalar case of axial shear waves in the composite material. Several limiting cases of interest are recovered.