On the propagation of acceleration waves in thermoelastic micropolar medias

Victor A. Eremeyev (1) , Leonid P. Lebedev (2) , Leonardo A. Rendón (2)

1 SFEDU - Southern Federal University [Rostov-on-Don]
2 Universidad Nacional de Colombia

The conditions for propagation of accelerating waves in a general nonlinear thermoelastic micropolar media are established. Deformation of micropolar media is described by the time-varying displacement vector r(t) and tensor of microrotation r(t) at each point. We call a surface S(t) an accelerating wave (or a singular surface for a solution of the dynamic problem for the medium) if the points are points of continuity of both r(t) and H(t) and their first spatial and time derivatives while the second spatial and time derivatives (acceleration) of r(t) and H(t) have jumps on S(t) (meaning that their one-sided limits at S(t) differ). So S(t) carries jumps in the acceleration fields as it propagat es through the body. In the thermomechanics of a micropolar continuum, similar propagating surfaces of singularities can exist for the fields of temperature, heat flux, etc. We establish the kinematic and dynamic compatibility relations for the singular surface S(t) in a nonlinear micropolar thermoelastic medium. An analog of Fresnel--Hadamard--Duhem theorem and an expression for the acoustic tensor are derived.

Domaines: Electronique

Victor A. Eremeyev, Leonid P. Lebedev, Leonardo A. Rendón. On the propagation of acceleration waves in thermoelastic micropolar medias. Revista Colombiana de Matemáticas, 2007, 41 (2), pp.397-406. ⟨hal-00831558⟩