Numerical analysis of wave propagation in fluid-filled deformable tubes (2013)
The theory of Biot describing wave propagation in fluid saturated porous media is a good effective approximation of a wave induced in a fluid-filled deformable tube -- Nonetheless, it has been found that Biot’s theory has shortcomings in predicting the fast P-wave velocities and the amount of intrinsic attenuation -- These problems arises when complex mechanical interactions of the solid phase and the fluid phase in the micro-scale are not taken into account -- In contrast, the approach proposed by Bernabe does take into account micro-scopic interaction between phases and therefore poses an interesting alternative to Biot’s theory -- A Wave propagating in a deformable tube saturated with a viscous fluid is a simplified model of a porous material, and therefore the study of this geometry is of great interest -- By using this geometry, the results of analytical and numerical results have an easier interpretation and therefore can be compared straightforward -- Using a Finite Difference viscoelastic wave propagation code, the transient response was simulated -- The wave source was modified with different characteristic frequencies in order to gain information of the dispersion relation -- It was found that the P-wave velocities of the simulations at sub-critical frequencies closely match those of Bernabe’s solution, but at over-critical frequencies they come closer to Biot’s solution