Forced Vertical Vibration of Rigid Circular Disc on a Transversely Isotropic Half-Space
Publication: Journal of Engineering Mechanics
Volume 136, Issue 7
Abstract
Vertical vibration of a rigid circular disc attached to the surface of a transversely isotropic half-space is considered in such a way that the axis of material symmetry is normal to the surface of the half-space and parallel to the vibration direction. By using Hankel integral transforms, the mixed boundary-value problem is transformed to a pair of integral equations termed dual integral equations in the literature, which generally can be reduced to a Fredholm integral equation of the second kind. With the aid of complex variable or contour integration the governing integral equation is numerically solved in the general dynamic case. The reduced static case of the dual integral equations is solved analytically and the vertical displacement, the contact pressure, and the static impedance/compliance function are explicitly solved. The dynamic contact pressure under the disc and the impedance function are numerically evaluated, and it is shown that the singularity that exists at the edge of the disc is the same as the one obtained for the static case. In addition, the impedance functions evaluated here are identical to the solution given by Luco and Mita for the isotropic domain. To show the effect of different material anisotropy, the numerical evaluations are given for some different transversely isotropic materials and compared.
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Acknowledgments
The first writer gratefully acknowledges Professor Stein Sture for his comments and suggestions for improving the manuscript of this paper. The partial support from the University of Tehran to M. E.-G. during this work is gratefully acknowledged.
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Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 136 • Issue 7 • July 2010
Pages: 913 - 922
Copyright
© 2010 ASCE.
History
Received: Jun 16, 2008
Accepted: Oct 28, 2009
Published online: Nov 9, 2009
Published in print: Jul 2010
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