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Analytical Solution of Coupled Thermoelastic Axisymmetric Transient Waves in a Transversely Isotropic Half-Space

[+] Author and Article Information
M. Raoofian Naeeni

Department of Surveying and Geomatics Engineering,
Center of Excellence in Geomatics,
Engineering and Disaster Prevention,
College of Engineering,
University of Tehran,
11155-4563 Tehran, Iran

M. Eskandari-Ghadi

Associate Professor
School of Civil Engineering,
College of Engineering,
University of Tehran,
11155-4563 Tehran, Iran

Alireza A. Ardalan

Professor
Department of Surveying and Geomatics Engineering,
Center of Excellence in Geomatics,
Engineering and Disaster Prevention,
College of Engineering,
University of Tehran,
11155-4563 Tehran, Iran

M. Rahimian

Professor

Y. Hayati

School of Civil Engineering,
College of Engineering,
University of Tehran,
11155-4563 Tehran, Iran

Manuscript received December 23, 2011; final manuscript received October 1, 2012; accepted manuscript posted October 8, 2012; published online January 25, 2013. Assoc. Editor: Martin Ostoja-Starzewski.

J. Appl. Mech 80(2), 024502 (Jan 25, 2013) (7 pages) Paper No: JAM-11-1492; doi: 10.1115/1.4007786 History: Received December 23, 2011; Revised October 01, 2012; Accepted October 08, 2012

A half-space containing transversely isotropic thermoelastic material with a depth-wise axis of material symmetry is considered to be under the effects of axisymmetric transient surface thermal and forced excitations. With the use of a new scalar potential function, the coupled equations of motion and energy equation are uncoupled, and the governing equation for the potential function, is solved with the use of Hankel and Laplace integral transforms. As a result, the displacements and temperature are represented in the form of improper double integrals. The solutions are also investigated in detail for surface traction and thermal pulses varying with time as Heaviside step function. It is also shown that the derived solutions degenerate to the results given in the literature for isotropic materials. Some numerical evaluations for displacement and temperature functions for two different transversely isotropic materials with different degree of anisotropy are presented to portray the dependency of response on the thermal properties as well as the degree of anisotropy of the medium.

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Figures

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Fig. 1

Transversely isotropic thermoelastic half-space under arbitrary surface tractions and flux

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Fig. 2

Surface radial displacement of an elastic Poisson material (material 1) subjected to a point force varying with time as a Heaviside step function

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Fig. 3

Surface vertical displacement of an elastic Poisson material (material 1) subjected to a point force varying with time as a Heaviside step function

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Fig. 4

Normalized surface radial displacement of transversely isotropic thermoelastic material 2 under the application of point force varies with time as a Heaviside step function

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Fig. 7

Normalized surface temperature change for transversely isotropic thermoelastic material 3, under the application of point heat source varies with time as a Heaviside step

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Fig. 6

Normalized surface vertical displacement of material 3, under the application of point heat flux varies with time as a Heaviside step function

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Fig. 5

Normalized surface temperature change of transversely isotropic material 3 under the application of point force varying with time as a Heaviside step function

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