Lyapunov stable torsional wave in multi-permeable porous viscoelastic media with sliding contact interface

Abstract

This study investigates torsional wave propagation in a complex geophysical configuration consisting of a homogeneous, isotropic, initially stressed, fluid-saturated multi-porous viscoelastic layer with multi-permeability overlying a transversely isotropic, heterogeneous viscoelastic half-space. The interface permits sliding contact, and the boundary surface is corrugated. Surface irregularity is represented using trigonometric functions, while binomial variations model heterogeneity in density and shear modulus. By employing separation of variables, the governing equations reduce to modified Bessel-type differential equations, enabling the derivation of a closed-form dispersion relation via asymptotic expansions. The formulation is validated by recovering the classical Love-wave dispersion relation as a limiting case. To assess numerical accuracy and corroborate the analytical results, linear and quadratic finite-element models are developed, and displacement fields and dispersion curves are compared.Furthermore, the stability of the resulting semi-discrete finite-element formulation is rigorously investigated through an energy-based Lyapunov framework, and the associated spectral characteristics of the assembled global damping and stiffness matrices are utilized to identify parameter-dependent stable and unstable regimes. Parametric analyses for a fractured triple-porous medium demonstrate that porous architecture, material properties, interface sliding, and boundary geometry significantly influence torsional wave characteristics. Convergence is quantified through L2 and energy norms, as well as relative L2 error norms under mesh refinement. In addition, frequency-domain measures, including energy flux, dissipated energy density, and quality factor, provide further physical insight into the attenuation mechanisms and energy transport within the proposed multi-porous viscoelastic medium. The results are pertinent to geophysical applications and structural engineering problems involving heterogeneous media and complex boundary conditions. © 2026