Elastodynamic Potential Method for Transversely Isotropic Solid
Publication: Journal of Engineering Mechanics
Volume 133, Issue 10
Abstract
A theoretical formulation is presented for the determination of the displacements, strains, and stresses in a three-dimensional transversely isotropic linearly elastic medium. By means of a complete representation using two displacement potentials, it is shown that the governing equations of motion for this class of problems can be uncoupled into a fourth-order and a second-order partial differential equation in terms of the spatial and time coordinate under general conditions. Compatible with Fourier expansions and Hankel transforms in a cylindrical coordinate system, the formulation includes a complete set of transformed displacement-potential, strain-potential, and stress-potential relations that can be useful in a variety of elastodynamic as well as elastostatic problems. As an illustration of the application of the method, the solution for a half-space under the action of arbitrarily distributed, time-harmonic surface traction is derived, including its specialization to uniform patch loads and point forces. To confirm the accuracy of the numerical evaluation of the integrals involved, numerical results are also included for cases of different degree of the material anisotropy, frequency of excitation, and compared with existing solutions.
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Acknowledgments
This work has been partially supported by the University of Science and Technology of Mazandaran through Grant No. UNSPECIFIEDA-185372, which is gratefully acknowledged.
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Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 133 • Issue 10 • October 2007
Pages: 1134 - 1145
Copyright
© 2007 ASCE.
History
Received: Aug 24, 2006
Accepted: Mar 9, 2007
Published online: Oct 1, 2007
Published in print: Oct 2007
Notes
Note. Associate Editor: Bojan B. Guzina
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