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Transient thermo‐elastic disturbances in a visco‐elastic semi‐space due to moving internal heat source

Kh. Lotfy (Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt and Department of Mathematics, Faculty of Science and Arts, Qassim University, Al‐mithnab, Kingdom of Saudi Arabia)

International Journal of Structural Integrity

ISSN: 1757-9864

Article publication date: 30 August 2011



This paper aims to investigate the transient disturbances created by an internal line heat source that suddenly starts moving uniformly inside a visco‐elastic half‐space.


Generalised theory of thermo‐elasticity with relaxation time proposed by Lord‐Shulman is applied. The material of the semi‐infinite medium is an isotropic visco‐elastic solid of Kelvin‐Voight type. Fourier and Laplace transform techniques are used.


Applying the Fourier and Laplace transform techniques, expressions for displacement components in the transformed domain are found. These expressions prove the existence of three waves – a modified thermal wave, a visco‐elastic wave of defused nature and a transverse visco‐elastic wave.

Research limitations/implications

Surface displacement components were evaluated on the boundary for only a short time.


The paper provides numerical results that are illustrated graphically to highlight the variations of surface displacement components with distance for different values of time, source depth and velocity of the source.



Lotfy, K. (2011), "Transient thermo‐elastic disturbances in a visco‐elastic semi‐space due to moving internal heat source", International Journal of Structural Integrity, Vol. 2 No. 3, pp. 264-280.



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