On the characterization and stability of plane waves under hyperbolic two-temperature generalized thermoelasticity

Abstract

The propagation and stability (Whitham’s criteria) of harmonic plane waves are described in the context of the hyperbolic two-temperature generalized thermoelasticity in which heat conduction in deformable bodies depends upon the difference between the double derivative of conductive and dynamic temperature. The exact dispersion relation solutions for the longitudinal plane wave are derived analytically. Several characterizations of the wave field, like phase velocity, specific loss, penetration depth, amplitude coefficient factor, and phase shift are examined for the low as well as high frequency asymptotic expansions. For the validity of analytical findings and to study the effect of varying hyperbolic two-temperature parameter on different characterizations, the numerical computation of a particular example is illustrated and displayed graphically. The results of some earlier works have been deduced and discussed from the present investigation as special$/$limiting cases.

Keywords:

• Asymptotic expansions
• dispersion relation
• hyperbolic two-temperature generalized thermoelasticity
• plane harmonic waves
• Whitham’s stability criteria

Acknowledgments

The authors are grateful to the reviewers for their encouraging and constructive comments and suggestions which improved the quality of the paper.

Additional information

Funding

The author Rashmi Prasad is thankful to UGC, New Delhi for the financial support.