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Structural Engineering and Mechanics Volume 93, Number 4, February25 2025 , pages 287-301 DOI: https://doi.org/10.12989/sem.2025.93.4.287 |
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Fundamental solution, boundary value problems and vibration of waves in photothermoelastic with diffusion and microtemperature |
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Rajneesh Kumar, Nidhi Sharma and Supriya Chopra
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| Abstract | ||
| In this paper, a new mathematical model of linear dynamic theory of photothermoelastic with diffusion and microtemperature is considered. The governing equations are made dimensionless, which are expressed in terms of elementary functions by assuming time harmonic variation of the field variables (displacement, temperature distribution, chemical potential and carrier density distribution). Fundamental solutions are constructed for the system of equations for steady oscillation. The internal and external boundary value problems (BVPs) of steady vibrations are formulated. The Green's first identity in the assumed model is also obtained. In the second part, the vibration of plane waves is 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 five longitudinal wave (P-wave), thermal wave(T-wave), mass diffusive wave (MD- wave), plasma wave(N-waves), longitudinal microtemperature wave (MT-wave), which advance with the distinct speeds, and one transverse wave which is free from thermal, mass diffusive, microtemperature and carrier density response. The attributes of waves i.e., phase velocity and attenuation coefficient are plotted in figures for the two models (i) with microtemperature (WMT), (ii) without microtemperature (WOMT). Various particular cases of interest are also deduced from the present investigations. The result obtained in this study should be useful for researchers who are working on thermodynamic energy, material science and hyperbolic thermoelastic models. | ||
| Key Words | ||
| BVPs; diffusion; fundamental solution; Green's formula; microtemperature; Photothermoelastic isotropic; plane waves; steady oscillations | ||
| Address | ||
| Rajneesh Kumar: Department of Mathematics, Kurukshetra University, Kurukshetra, Haryana, India Nidhi Sharma, Supriya Chopra: Department of Mathematics, Maharishi Markandeshwar University Mullana, Ambala, Haryana, India; 3Department of Mathematics, Government College for Women, Ambala City, Haryana, India | ||