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Representation of fundamental solution and vibration of waves in photothermoelastic under MGTE model

  • Rajneesh Kumar (Department of Mathematics, Kurukshetra University) ;
  • Nidhi Sharma (Department of Mathematics, Maharishi Markandeshwar University Mullana) ;
  • Supriya Chopra (Department of Mathematics, Maharishi Markandeshwar University Mullana) ;
  • Anil K. Vashishth (Department of Mathematics, Kurukshetra University)
  • Received : 2022.10.23
  • Accepted : 2023.04.08
  • Published : 2023.06.25
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Abstract

In this paper, Moore-Gibson-Thompson theory of thermoelasticity is considered to investigate the fundamental solution and vibration of plane wave in an isotropic photothermoelastic solid. The governing equations are made dimensionless for further investigation. The dimensionless equations are expressed in terms of elementary functions by assuming time harmonic variation of the field variables (displacement, temperature distribution and carrier density distribution). Fundamental solutions are constructed for the system of equations for steady oscillation. Also some preliminary properties of the solution are explored. In the second part, the vibration of plane waves are examined by expressing the governing equation for two dimensional case. It is found that for the non-trivial solution of the equation yield that there exist three longitudinal waves which advance with the distinct speed, and one transverse wave which is free from thermal and carrier density response. The impact of various models (i)Moore-Gibson-Thomson thermoelastic (MGTE)(2019), (ii) Lord and Shulman's (LS)(1967) , (iii) Green and Naghdi type-II(GN-II)(1993) and (iv) Green and Naghdi type-III(GN-III)(1992) on the attributes of waves i.e., phase velocity, attenuation coefficient, specific loss and penetration depth are elaborated by plotting various figures of physical quantities. Various particular cases of interest are also deduced from the present investigations. The results obtained can be used to delineate various semiconductor elements during the coupled thermal, plasma and elastic wave and also find the application in the material and engineering sciences.

Keywords

Acknowledgement

Authors are thankful to the reviewers for their valuable suggestions which helped the author's improve the quality of manuscript.

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