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Dynamic Greenís Functions of an Axisymmetric Thermoelastic Half-Space by a Method of Potentials

Yazdan Hayati
Morteza Eskandari-Ghadi
Mehdi Raoofian
Mohammad Rahimian
Alireza A. Ardalan
Journal / Anthology

Journal of Engineering Mechanics
Year: 2013
Volume: 139
Issue: 9
Page range: 1166-1177

With the aid of a new complete scalar potential function, an analytical formulation for thermoelastic Greenís functions of an axisymmetric linear elastic isotropic half-space is presented within the theory of Biotís coupled thermoelasticity. By using the potential function, the governing equations of coupled thermoelasticity are uncoupled into a sixth-order partial differential equation in a cylindrical coordinate system. Then, by using Hankel integral transforms to suppress the radial variable, a sixth-order ordinary differential equation is received. By solving this equation and considering boundary conditions, displacements, stresses, and temperature are derived in the Hankel integral transformed domain. By applying the theorem of inverse Hankel transforms, the solution is obtained generally for arbitrary surface timeharmonic traction and heat distribution. Subsequently, point-load Greenís functions for the displacements, temperature, and stresses are given in the form of some improper line integrals. For more investigations, the solutions are also determined analytically for uniform patch-load and patch-heat distributed on the surface. For validation, it is shown that the derived solutions could be degenerated to elastodynamic and quasistatic thermoelastic cases reported in the literature. Numerical evaluations of improper integrals, which have some branch points and pole, are carried out using a suitable quadrature scheme by Mathematica software. To show the accuracy and efficiency of numerical algorithm, a numerical evaluation from this study is compared with the results of an existing elastodynamic case, where excellent agreement is achieved.


Greenís function, Wave propagation, Axisymmetric, Thermoelastodynamic, Potential method