Meccanica (2012) 47:1337–1347 DOI 10.1007/s11012-011-9517-y Thermoelastic plane waves for an elastic solid half-space under hydrostatic initial stress of type III Mohamed I.A. Othman · Sarhan Y. Atwa Received: 2 July 2009 / Accepted: 4 November 2011 / Published online: 7 December 2011 © Springer Science+Business Media B.V. 2011 Abstract In this paper, we constructed the equations of generalized thermoelastic isotropic and homoge- neous half-space under hydrostatic initial stress in the context of the Green and Naghdi (GN) theory of types II and III. Normal mode analysis is used to ob- tain the exact expressions of temperature, displace- ment and stress. Comparisons are made with the re- sults predicted by GN theory of types II and III in the presence and absence of the hydrostatic initial stress. The temperature, displacement and stress distributions are represented graphically. M.I.A. Othman ( ) · S.Y. Atwa Faculty of Science, Department of Mathematics, Zagazig University, P.O. Box 44519, Zagazig, Egypt e-mail: m_i_othman@yahoo.com S.Y. Atwa e-mail: srhan_1@yahoo.com S.Y. Atwa Higher Institute of Engineering, Dep. of Eng. Math. and Physics, Shorouk Academy, El Shorouk, Egypt S.Y. Atwa Faculty of Science, Department of Maths., Shaqra University, P.O. Box 102, Al-Qowyiyaia, Saudi Arabia M.I.A. Othman Department of Mathematics, Faculty of Science, Shaqra University, Al-Dawadme 11911, P.O. Box 1040, Kingdom of Saudi Arabia Keywords Hydrostatic · Initial stress · GN theory · Types II and III · Generalized thermoelasticity · Normal mode analysis 1 Introduction The classical theory of thermoelasticity as exposed, for example, in Carlson’s article [1] has been gener- alized and modified into various thermoelastic models that run under the label of hyperbolic thermoelastic- ity (see the survey of Chandrasekharaiah, [2] and Het- narski and Ignazack, [3]). Lord and Shulman (L-S) [4] introduced the the- ory of generalized thermoelasticity with one relaxation time by postulating a new law of heat conduction to re- place the classical Fourier law. This new law contains the flux vector as well as its time derivative. It contains also a new constant that acts as a relaxation time. The heat equation of this theory is of the wave-type, en- suring finite speeds of propagation for heat and elas- tic waves. The remaining governing equations for this theory, namely, the equations of motions and the con- stitutive relations, remain the same as those in the cou- pled and the uncoupled theories. Müller [5] first intro- duced the theory of generalized thermoelasticity with two relaxation times. A more explicit version was then introduced by Green and Laws [6], Green and Lindsay [7] and independently by Suhubi [8]. In this theory the temperature rates are considered among the constitu- tive variables. This theory also predicts finite speeds