, Volume 52, Issue 8, pp 1935–1945 | Cite as

Generalized solutions of transient thermal shock problem with bounded boundaries

  • Y. Z. WangEmail author
  • D. Liu
  • Q. Wang
  • J. Z. Zhou


In this work, the generalized thermoelastic solutions with bounded boundaries for the transient shock problem are proposed by an asymptotic method. The governing equations are taken in the context of the generalized thermoelasticity with one relaxation time (L–S theory). The general solutions for any set of boundary conditions are obtained in the physical domain by the Laplace transform techniques. The corresponding asymptotic solutions for a thin plate with finite thickness, subjected to different sudden temperature rises in its two boundaries, are obtained by means of the limit theorem of Laplace transform. In the context of these asymptotic solutions, two specific problems with different boundary conditions have been conducted. The distributions of displacement, temperature and stresses, as well as the propagations, intersections and reflections of two elastic waves, named as thermoelastic wave and thermal wave separately, are obtained and plotted. These results are agreed with the results obtained in the existing literatures.


Generalized thermoelasticity Asymptotic solutions Transient thermal shock Bounded boundary conditions Thin plate 



This research was supported by the National Natural Science Foundation of China (Grant Nos. 11102073, 51206062), the Jiangsu Overseas Research and Training Program for University Prominent Young and Middle-aged Teachers and Presidents, and the Priority Academic Program Development of Jiangsu Higher Education Institutions.


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Department of Energy and Power EngineeringJiangsu UniversityZhenjiangChina
  2. 2.Department of Mechanical EngineeringJiangsu UniversityZhenjiangChina

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