Earth and Planetary Science

Modeling of Waves on a Dual-Porous Pre-Stressed Transversely Isotropic Impedance and Irregular Boundary Medium with Thermal and Dual Pore Sources

anya Anya

Department of Mathematical Sciences, Faculty of Natural and Applied Sciences, Veritas University Abuja, Bwari-Abuja, Nigeria

DOI: https://doi.org/10.36956/eps.v4i1.2008

Received: 16 April 2025; Published: 30 June 2025

Abstract

Occurrences in the forms of vibrational phenomena have both positive and negative impacts on the Earth’s crust and materials. Scientists in the field of seismology and emerging technologies often hinge their innovations and applications on the nature of material compositions. Owing to this, we present in this work a surface wave solution that results from a dual-porous pre-stressed transversely isotropic impedance medium with an irregular boundary under heat stress based on Green-Lindsay thermoelasticity, and derived through the principles of mathematical analysis associated with wave motion. The irregularity of the boundary is assumed to be in the form of a corrugated surface. This is represented as a trigonometric Fourier series in which the wave number and the amplitude associated with the corrugated surface of the medium affect the motion of the wave. Moreover, initial stress and dual porosity sources are incorporated into the modeled problem to enrich its physical composition. Due to the satisfaction of the adopted displacement components within the classical wave equation, we employed the harmonic solution method to find the analytical solution and perform analysis on the modeled equations of motion. Following this, we derived the fundamental analytical solution for the various distributions of double porosities, thermal flux, shear and normal stresses, and displacement components of the surface wave on the transversely isotropic material. We demonstrate the dependency of the wave propagation on these interacting physical quantities including dual porosities, initial stress and the grooved boundary surface parameters such as the wave number and amplitude of material’s corrugation. Thus, it suffices to state that researchers in geophysics, material sciences, and mechatronics applications, among others, would find this model useful.

Keywords: Transversely Isotropic Material, Grooved Boundary, Impedance, Initial Stress, Thermal Stress, Double-Porosity

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