Frequency Domain Analysis of an Axisymmetric Thermoelastic Transversely Isotropic Half-Space
Publication: Journal of Engineering Mechanics
Volume 139, Issue 10
Abstract
By virtue of a new complete scalar potential function, an analytical formulation is presented to determine displacements, stresses, and temperature in an axisymmetric linear thermoelastic transversely isotropic half-space affected by time harmonic surface axisymmetric vertical traction and/or surface heat flux. With the use of only one scalar potential function in a cylindrical coordinate system, the coupled partial differential equations in thermoelasticity are transformed to a sixth-order partial differential equation governing the potential function. Then, by using the Hankel integral transforms, a sixth-order ordinary differential equation is received, which after solving, results in the displacements, stresses, and temperature fields. To prove the validation of the analytical solution presented in this paper, the solutions are reduced to the case of elastodynamics in transversely isotropic half-space and in a quasi-static thermoelastic isotropic half-space, where exact agreements with the solutions reported in the literature are achieved. Because of complexity of the integrands, numerical evaluations of the integrals involved in this paper are carried out using a suitable quadrature scheme by Mathematica software. To show the accuracy and efficiency of the numerical algorithm, the solution of this study is compared with the results of an existing elastodynamic transversely isotropic half-space, where an excellent agreement is achieved.
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Acknowledgments
The partial support from University of the Tehran to M. Eskandari-Ghadi during this work is gratefully acknowledged.
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Published In
Journal of Engineering Mechanics
Volume 139 • Issue 10 • October 2013
Pages: 1407 - 1418
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Aug 25, 2012
Accepted: Dec 5, 2012
Published online: Dec 7, 2012
Published in print: Oct 1, 2013
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