On the dispersion of waves for the linear thermoelastic relaxed micromorphic model

Abstract

We present the complete set of constitutive relations and field equations for the linear thermoelastic relaxed micromorphic continuum and investigate its variants for wave propagation. It is found that the additional thermal effects give rise to new waves and generate couplings with longitudinal waves which are not existing in the relaxed micromorphic continuum without thermal effects. However, transverse waves go unaffected by the thermal properties. Thermal effects do not create any band gap in the dispersion curves of the model with three curvature parameters. The dispersion curves have been computed numerically for a particular model and compared with those presented in earlier studies.

Keywords:

• Micromorphic
• dispersion
• thermal
• wave
• acoustic
• optic
• band gap
• metamaterials
• linear heat equation

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 In the classical micromorphic model, m would be a third-order tensor.