Plane wave propagation and fundamental solution in functionally graded couple stress micropolar thermoelastic solid with diffusion and voids

Abstract

In the present problem, we study plane wave propagation and establish fundamental solution in the theory of functionally graded couple stress micropolar thermoelastic solid with diffusion and voids. We observe that there exists a set of four coupled waves namely plane wave(P), thermal wave(T), mass diffusion wave(MD), rotational wave(R) and a set of two coupled waves namely transverse waves(SV1 and SV2) with different phase velocities. The effect of couple stress and voids on phase velocity, attenuation coefficient, penetration depth and specific loss has been studied numerically and presented graphically with respect to angular frequency. It has been observed that characteristics of all the waves are influenced by couple stress and void parameter. Fundamental solution of differential equations of motion in case of steady oscillations has been constructed by using vector calculus and various numerical approaches. Deductions has been made from the present work and compared with the existing result. The analysis of fundamental solution is very helpful to investigate the various problems of functionally graded couple stress micropolar thermoelastic solid with diffusion and voids. The graphical analysis of present study is also very beneficial in order to study the different fields of geophysics, electronics and aerospace like seismology, volcanology, telecommunication, manufacturing of aircrafts etc.