On wavenumbers of plane harmonic type III thermoelastic waves

The present study is devoted to propagation of plane harmonic GNIII-thermoelastic waves by the coupled system of linear equations of motion and heat transport based on the Green & Naghdi theory of thermoelasticity. Analytical findings and exact solutions are primarily related to complex wavenumbers, phase velocities and attenuation coefficients of the plane GNIII-thermoelastic waves. Complete analysis of all analytical branches of the wavenumbers is given. Constitutive inequlities and frequency restrictions which provide a normal behaviour of the plane GNIII-thermoelastic waves are obtained. Limiting cases, including those corresponding to GNI/CTE (the classical theory) and GNII (hyperbolic, thermal energy conserving theory) thermoelasticity, are noted. The paper presents an in-depth analysis of plane thermoelastic waves in the context of GNI, II, III.