Thermoelastic slowness surfaces in anisotropic media with thermal relaxation

Abstract

Analysis for general closed form solution of the thermoelastic waves in anisotropic heat conducting materials is obtained by using the solution technique for the biquadratic equation in the framework of the generalized theory of thermoelasticity. Obtained results are general in nature and can be applied to the materials of higher symmetry classes such as transvesely isotropic, cubic, and isotropic materials. Uncoupled and coupled thermoelasticity are the particular cases of the obtained results. Numerical computations are carried out on a fiber reinforced heat conducting composite plate modeled as a transversely isotropic media. The two dimensional slowness curves corresponding to different thermal relaxations are presented graphically and characteristics displayed are analyzed with thermal relaxations. Keywords Slowness Surfaces; thermoelasticity; anisotropic; coupled and thermal relaxation times.Thermoelastic slowness surfaces in anisotropic media with thermal relaxation INTRODUCTIONMost materials experience volumetric variations when are subjected to temperature variations and the consequent thermal stresses developed due to temperature gradient in the surface vicinity results in micro-crack and others imperfection development at the surface of anisotropic materials. Thus owing to anisotropic material's applications in aeronautics, astronautics, plasma physics, nuclear reactors and high-energy particle and in various others engineering sciences, theory of thermoelasticity has aroused intense attention in our challenge to understand the nature of the interaction between temperature and strain fields. Main characteristics of the waves when they propagate within an anisotropic media are: phase and group velocities depend on direction -anisotropy, there is a difference between the phase velocity (propagation of the wave) and the group velocity (propagation of energy), occur shear wave splitting. Since the last century generation of waves in thermoelasticity is already known by chopping the sunlight coming onto a heat conduct-

New Hydrogels Based on Agarose/Phytagel and Peptides

“…These major differences indicate changes in the amine group through its interaction with the gellan carboxylate group. [ 26 ]…”

“…Initially, 2% Phytagel and 0.5% Agarose solutions were prepared in 0.01 m sodium phosphate buffer (pH = 7.4). Next, two individual solutions of Fmoc‐Lys‐Fmoc and Fmoc‐Gly‐Gly‐Gly were prepared by dissolving them in DMSO/PBS 7.4 as previously presented [ 26 ] and mixed in a 1:1 volumetric ratio. The mixture between Fmoc‐Lys‐Fmoc and Fmoc‐Gly‐Gly‐Gly (Fmoc‐Lys‐Fmoc_Fmoc‐Gly‐Gly‐Gly) was added over the Phytagel or the agarose solution, under slightly stirring, thus obtaining the hybrid hydrogels, namely, Fmoc‐Lys‐Fmoc_Fmoc‐Gly‐Gly‐Gly_Phytagel and Fmoc‐Lys‐Fmoc_Fmoc‐Gly‐Gly‐Gly_Agarose gels.…”

Simulation of 3D wave propagation in thermoelastic anisotropic media

“…Let us define by (x, y, z) the position vector, t the time variable, v i , i = 1,2,3 the components of the particle velocity field, by σ ij the components of the stress tensor and by T the increment of temperature above a reference absolute temperature T 0 for the state of zero stress and strain. In orthorhombic media, the stress-strain relations of thermoelasticity are given by (Banerjee and Pao, 1974;Verma, 2001Verma, , 2002Verma, , 2014:…”

“…Tokuoka (1973) considered plane waves, while Banerjee and Pao (1974) performed a detailed plane-wave analysis, showing the four wavefronts present in thermoelastic-anisotropic media. Other authors who tackled the problem are Dhaliwal and Sherief (1980), Kolyano and Shter (1982) and Verma (2001Verma ( , 2002Verma ( , 2014.…”

The Propagation of Thermoelastic Waves in Anisotropic Media of Orthorhombic, Hexagonal, and Tetragonal Syngonies

“…Verma analytically investigated problem propagation of thermoelastic wave along arbitrary direction in a heat conducting plate by employing the normal mode expansion method, available in generalized theory of thermoelasticity having single thermal relaxation time [8].…”