Reflection and transmission of transient ultrasonic wave in fractal porous material: Application of fractional calculus

International audienceThis paper provides a time domain model for the propagation of transient ultrasonic waves in a self-similar porous material having a rigid frame. This model is based on the formalism of Stillinger-Palmer-Stavrinou, which consists in modeling the fractal material as a porous medium with a non-integer dimensional space. This paper is devoted to the time-domain analytical calculus of the reection and transmission operators that are expressed in terms of Mittag-Leer functions. A sensitivity numerical study using ultrasonic reected and transmitted waves is performed, highlighting the eect of of the material's physical parameters (fractal dimension, tortuosity, viscous characteristic length and porosity) on the waveforms