Characteristic Constitutive Numbers in Semi-Isotropic Coupled Thermoelasticity

In continuum mechanics (especially in hydroaeromechanics), methods of modeling flow (deformation) by characteristic numbers are widely used. The present study is devoted to the search for characteristic combinations of constitutive thermoelastic modules, geometric and thermomechanical parameters of the boundary value problem. Modeling the micropolar solids deformation by characteristic numbers is characterized by a sufficiently large number (13) of constitutive modules. The constitutive equations, the dynamic equations and the heat conduction equation for a semi-isotropic micropolar thermoelastic continuum are derived in a linear approximation. A dimensional analysis of the governing system of differential equations is carried out. A physically consistent sets (9 primary and several arbitrary) of dimensionless characteristic combinations of constitutive constants is proposed. The characteristic numbers for harmonic waves propagating along the axis of a stress free thermally insulated long cylindrical semi-isotropic thermoelastic waveguide are obtained and discussed.