Propagation of waves in transversely isotropic micropolar generalized thermoelastic half space ☆ Rajneesh Kumar ⁎, Rajani Rani Gupta Department of Mathematics, Kurukshetra University, Kurukshetra, Haryana 136 119, India abstract article info Available online 27 August 2010 Keywords: Micropolar Transversely isotropic Amplitude ratios Generalized thermoelastic The propagation of waves in a transversely isotropic micropolar medium possessing thermoelastic properties based on Lord and Shulaman (L–S), Green and Lindsay (G–L) and Coupled thermoelasticity (C-T) theories are discussed. After developing the solution, the phase velocities and attenuation quality factor have been obtained. The expressions for amplitudes of stresses, displacements, microrotation and temperature distribution have been derived and computed numerically. The numerical results have been plotted graphically. © 2010 Elsevier Ltd. All rights reserved. 1. Introduction Material is endowed with microstructure, like atoms and molecules at microscopic scale and grains, fibers or particulate at mesoscopic scale. Homogenization of a basically heterogeneous material depends on scale of interest. When stress fluctuation is small enough compared to the microstructure of the material, homogenization can be made without considering the detailed microstructure of the material. However, if this is not the case, the microstructure of material must be considered properly in a homogenized formulation [1,2]. The concept of microcontinuum, proposed by Eringen [1], takes into account the microstructure of material while the theory itself remains still in a continuum formulation. The first grade microcontinuum consists of a hierarchy of theories, such as, micropolar, microstretch and micro- morphic, depending on how much micro-degrees of freedom is incorporated. These microcontinuum theories are believed to be potential tools to characterize the behavior of material with compli- cated microstructures. The most popular microcontinuum theory is a micropolar one, in this theory, a material point can still be considered as infinitely small, however, there are microstructures inside of this point. So, there are two sets of variable to describe the deformation of this material point, one characterizes the motion of the inertia center of this material point; the other describes the motion of the microstructure inside of this point. In micropolar theory, the motion of the microstructure is supposed to be an independent rigid rotation. Application of this theory can be found in [1,3]. The linear theory of micropolar thermoelasticity was developed by Eringen [4] and Nowacki [5] to include thermal effects and is known as micropolar coupled thermoelasticity. A comprehensive work has been done in the theory of micropolar thermoelasticity [6]. Boschi and Iesan [7] extended a generalized theory of micropolar thermoelasti- city that permits the transmission of heat as thermal waves at finite speed. The aim of the present paper is to discuss the propagation of waves in transversely isotropic micropolar generalized thermoelastic half space. The propagation of waves in micropolar materials has many applications in various fields of science and technology, namely, atomic physics, industrial engineering, thermal power plants, sub- marine structures, pressure vessel, aerospace, chemical pipes and metallurgy. The phase velocities and attenuation quality factors are obtained and plotted numerically for different theories of thermo- elasticity. The expressions for amplitude ratio of components of displacement, microrotation, stresses and temperature distribution are also obtained. Some special cases of interest are also deduced. 2. Basic equations The basic equations in dynamic theory of the plain strain of a homogeneous, transversely isotropic micropolar generalised thermo- elastic solid in absence of body forces, body couples and heat sources are given by: t ji;j = ρ :: u i ; ð1Þ m ik;i + ε ijk t ij = ρ| :: ϕ k ; i; j; k =1; 2; 3: ð2Þ International Communications in Heat and Mass Transfer 37 (2010) 1452–1458 ☆ Communicated by A.R. Balakrishnan. ⁎ Corresponding author. E-mail addresses: rajneesh_kuk@rediffmail.com (R. Kumar), rajani_gupta_83@rediffmail.com (R.R. Gupta). 0735-1933/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.icheatmasstransfer.2010.08.001 Contents lists available at ScienceDirect International Communications in Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ichmt