On Wave Solutions of Dynamic Equations of Hemitropic Micropolar Thermoelasticity

• Main Authors: Kovalev, Vladimir Aleksandrovich, Radaev, Yurii Nickolaevich
• Format: Article
• Language: English
• Published: Saratov State University 2019-12-01
• Series: Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
• Subjects: hemitropic; micropolar; thermoelastic; plane wave; wavenumber; polarization; athermal wave
• Online Access: https://mmi.sgu.ru/sites/mmi.sgu.ru/files/text-pdf/2020/04/454-463kovalev-radayev.pdf

Coupled equations of hemitropic thermoelastic micropolar continuum formulated in terms of displacement vector, microrotation vector and temperature increment are considered. Thermodiffusion mechanism of heat transport is assumed. Hemitropic thermoelastic constitutive constants are reduced to a minimal set retaining hemitropic constitutive behaviour. Coupled plane waves propagating in thermoelastic media are studied. Spatial polarizations of the coupled plane waves are determined. Bicubic equations for wavenumbers are obtained and then analyzed. Three normal complex wavenumbers for plane waves are found. Equations relating to the complex amplitudes of displacements, microrotations and temperature increment are obtained. Athermal plane waves propagation is also discussed. It is shown that polarization vectors and the wave vector are mutually orthogonal. Wavenumbers are found as roots of a biquadratic equation. For athermal plane wave depending on the case two or single real normal wavenumbers are obtained.