Mathematical Modeling of Waves in a Porous Micropolar Fibrereinforced Structure and Liquid Interface

Abstract

The present investigation envisages on the Mathematical modeling of waves propagating in a porous micropolar fibre-reinforced structure in a half-space and liquid interface. The harmonic method of wave analysis is utilized, such that, the reflection and transmission of waves in the media were modelled and it’s equations of motion analytically derived. It was deduced that incident longitudinal wave in the solid structure yielded four reflected waves given as; quasi–P wave (qLD), quasi–SV wave, quasi–transverse microrotational (qTM) wave and a wave due to voids and one transmitted wave known as the quasi-longitudinal transmitted (qLT) wave. The phase velocity in the liquid medium is independent of angle of propagation as observed. The corresponding amplitude ratios of propagations for both reflected and transmitted waves are analytically derived by employing Snell’s law. The model would prove to be of relevance in the understanding of modeling of the behavior of propagation phenomena of waves in micropolar fibre-reinforecd machination systems resulting in solid/liquid interfaces especially in earth sciences and in particular seismology, amongst others.

Keywords

• Micropolar, Fibre reinforced, Reflection/transmission, Voids/porosity, Liquid interface