Response of impedance parameters on waves in the micropolar thermoelastic medium under modified Green‐Lindsay theory

Abstract

The present study is focused on devoting a model to estimate the response of impedance parameters in micropolar with modified Green-Lindsay (MMGL) generalized thermoelastic medium. The problem of reflection phenomena is formulated and explained for the considered model. Amplitude ratios of various waves are obtained for the MMGL model, Green-Lindsay (G-L,1972) thermoelastic model, and Lord-Shulman (L-S,1967) thermoelastic model for longitudinal displacement wave (LD-wave), thermal wave (T-wave), coupled transverse (CD-I) wave and coupled micro-rotational (CD-II) wave. These amplitude ratios are the functions of the angle of incidence, frequency, and impedance parameters. The impact of impedance parameters on various reflection coefficients is displayed in the form of a graph. From the present study, certain cases are also deduced. 1Nomenclature: 𝜆, μ, Lame's constants; , γ 1 = (3𝜆 + 2𝜇 + K) 𝛼 t ,; 𝛼 t , the coefficient for linear thermal expansion,; K * , coefficient of thermal conductivity; t, time; t pq , components of stress; T, Temperature distribution; 𝜏 0 and 𝜏 1 , relaxation times; 𝛿 pq , Kronecker delta; 𝜌, C e , density, specific heat respectively; ⃗ u, displacement vector; 𝜂 1 , η 2 , η 3 and η 4 , constant; 𝜙 r , microrotation vector; 𝜉 pqr , alternating tensor; 𝛼, 𝛽, 𝛾, K, micropolar constants; T 0 , reference temperature; m pq , component of couple stress tensor; ∇ 2 , Laplacian operator.