Analysis of Reflection Phenomena in a Fiber Reinforced Piezo-Thermoelastic Half Space with Diffusion and Two-Temperature

Document Type : Research Paper


1 Department of Mathematics, Guru Jambheshwar University of Science and Technology, Hisar-125001, Haryana, India

2 Department of Basic and Applied Sciences, BPS Mahila Vishwavidyalaya, Khanpur Kalan, Sonepat-131305, Haryana, India



Present work is concerned with the analysis of transient wave phenomena in a piezo-thermoelastic medium with diffusion, fiber reinforcement and two-temperature, when an elastic wave is made incident obliquely at the traction free plane boundary of the considered medium. The formulation is applied under the purview of generalized theory of thermoelasticity with one relaxation time. The problem is solved analytically and it is found that there exists four coupled quasi waves: qp (quasi-p ), qMD (quasi mass diffusion), qT (quasi thermal) and qSV (quasi-SV ) waves propagating with different speeds in a two-dimensional model of the solid. The amplitude ratios, phase velocities and energy ratios for the reflected waves are derived and the numerical computations have been carried out with the help of MATLAB programming. Effect of presence of diffusion is analyzed theoretically, numerically and graphically. The number of reflected waves reduce to three in the absence of diffusion as qMD wave will disappear in that case which is physically admissible. Influence of piezoelectric effect, two temperature and anisotropy is discussed on different characteristics of reflected waves such as phase velocity and reflection coefficients. It has been verified that there is no dissipation of energy at the boundary surface during reflection. Thus, the energy conservation law holds at the surface. Finally, all the reflection coefficients are represented graphically through 3D plots to estimate and highlight the effects of frequency and angle of incidence.


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