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

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