Wave propagation in generalized thermo-microstretch elastic solid containing voids

Abstract

A linear theory of generalized thermo-microstretch elastic solid containing voids is formulated. Lord and Shulman [2] theory of thermoelasticity is employed to incorporate thermal effects. Free energy density function is constructed to develop the constitutive relations and field equations for an isotropic homogeneous generalized thermo-microstretch elastic solid containing voids. The possibility of propagation of plane waves is investigated in the medium of infinite extent. It is found that there may exist four sets of coupled longitudinal waves, two sets of coupled transverse waves and an independent longitudinal microrotational wave traveling with distinct speeds. Each set of coupled longitudinal waves is found to be attenuating and dispersive in nature, while an independent longitudinal microrotational wave and the remaining two sets of coupled transverse waves are found to be dispersive but non-attenuating in nature. All the possible waves are influenced by the polar property of the medium; however, all the coupled longitudinal waves are influenced by the stretch, voids and thermal properties of the medium. It is also found that all coupled longitudinal waves exist for all non-negative frequencies, while the independent longitudinal microrotational wave and one of the sets of coupled transverse waves exist only after certain cutoff frequency.

KEYWORDS:

• Dispersion
• microstretch
• plane waves
• relaxation time
• thermal
• voids

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Ms. Manisha is grateful to the Council of Scientific and Industrial Research, New Delhi for providing financial support in the form of Senior Research Fellowship through Grant no. F.09/135(0869)/2019-EMR-I. While Dr Dilbag Singh is grateful to the University Grants Commission and Department of Science and Technology, New Delhi for providing financial assistance through Start-Up Grant no. F.4-5 (69-FRP)/2014(BSR) and DST-FIST Grant no. SR/FST/MS-II/2019/43 to complete this study.