Propagation of acoustic waves in micro-polar porous medium.
Résumé
Generally, in acoustic propagation in porous media such as rocks or bone tissues, classical elasticity is used, in which the stresses are proportional to the deformations and only the translation aspect is taken into account. However, it has been shown that in these porous media, the rotational movement
of particles (solid or fluid) between them (gyration) is not negligible, and this is described by micro-polar theories. In this work, the acoustic wave propagation in micro-polar porous material in the high frequency range is studied. The fluid / structure and micro-polar couplings are well described in the Biot equations. The motion equations are solved in the frequency domain, thus obtaining the dispersion relations. Several propagation modes are highlighted, in addition to the two classical Biot waves and the shear wave, a micro-polar compression wave and a micro-polar shear wave are obtained. The phase velocities of these five waves are calculated and plotted against frequency. A sensitivity study of the micro-polar parameters on
these phase velocities is carried out. The relative movements of the internal structures of the solid and fluid thus described take into account the interactions between them and can improve the prediction of the Biot theory on the attenuation of the waves in the porous media. The energy transported by the wave
is distributed between compression, shear and "gyration" waves which are strongly
damped. The losses that are not modelized by the Biot Theory could partly be explained by the
attenuation of the gyration. In addition to the proposed theoretical study, an experimental method is
being developed to validate the theory.