Dispersion and attenuation of first and second sound waves under four models of Green-Naghdi generalized thermo-elasticity

Abstract

The dispersion and attenuation of first and second sound waves under four models of G-N generalized thermo-elasticity are studied in the present work. Among the various generalized thermo-elastic theories, the introduction of the conception of thermal displacement makes G-N generalized thermo-elasticity unique and hence gotten wide attentions and applications. There are three types of G-N generalized thermo-elasticity. Based the Type III, a modified model with three phase delay had also been proposed recently. However, a comprehensive investigation and an in-depth insight are lacking. The differences of the constitutive equations and the governing equations in the four models are remarked in the present work. The dispersive and attenuation properties of first and second sound waves (coupled thermo-elastic waves) are mainly studied. The amplitude ratio and the phase shift between the temperature field and the displacement field under four models are also analyzed. It is found that the type II leads to neither dispersive nor attenuation while other three models lead to both dispersive and the attenuation features. These detailed investigations reveal that type II is only a special case. Type III and its variation with three phase delay are the more general and flexible models and should get more attention.