Forced vertical vibration of four rigid strips on a semi-infinite elastic solid

In this paper, the problem of two-dimensional oscillations of four rigid strips, situated on a homogeneous isotropic semi-infinite elastic solid and forced by a specified normal component of the displacement has been considered. The mixed boundary value problem of determining the unknown stress distribution just below the strips and vertical displacement outside the strips has been converted to the determination of the solution of quadruple integral equations by the use of Fourier transform. An iterative solution of these integral equations valid for low frequency has been found by the application of the finite Hilbert transform. The normal stress just below the strips and the vertical displacement away from the strips have been obtained. Finally, graphs are presented which illustrate the salient features of the displacement and stress intensity factors at the edges of the strips. © 1997, Elsevier Science Ltd. All rights reserved