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Background <p>Rayleigh wave propagation in double-porous thermoelastic media remains insufficiently described by classical theories, particularly when memory-dependent thermal effects, long-range spatial interactions, and non-conservative energy dissipation are involved.</p> Purpose <p>This study aims to address this gap by introducing a unified Fractional Moore–Gibson–Thompson model with Klein–Gordon non-locality (FMGT–KG) for analyzing Rayleigh wave behavior in a double-porous thermoelastic medium.</p> Methods <p>A modified nonlocal Fourier law is formulated to incorporate fractional memory effects and spatial nonlocality. The governing equations are developed within the FMGT–KG framework and solved using an eigenvalue approach. Frequency equations are derived for both isothermal and thermally insulated surface conditions.</p> Results <p>The proposed model enables the numerical prediction of key wave characteristics, including wave speed (V), specific loss (SL), penetration depth (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\delta\)</EquationSource> </InlineEquation>), and attenuation (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(Q\)</EquationSource> </InlineEquation>). The results demonstrate the capability of the FMGT–KG framework to describe anomalous wave behavior more accurately than classical thermoelastic models.</p> Conclusion <p>The developed formulation provides a rigorous mathematical and physical framework for studying Rayleigh wave propagation in complex double-porous thermoelastic media. The findings are relevant to geophysical wave analysis, nondestructive material evaluation, and advanced modeling of dissipative wave phenomena.</p>

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Fractional Derivative of MGT Model for Rayleigh Waves Propagation in Thermoelastic Medium with Double Porosity under Klein–Gordon (KG) Nonlocality

  • 期刊论文

  • 发表日期：

    2026年6月2日

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  • Ibrahim-Elkhalil Ahmed,
  • Ahmed Yahya,
  • Adam Zakria

摘要

Background

Rayleigh wave propagation in double-porous thermoelastic media remains insufficiently described by classical theories, particularly when memory-dependent thermal effects, long-range spatial interactions, and non-conservative energy dissipation are involved.

Purpose

This study aims to address this gap by introducing a unified Fractional Moore–Gibson–Thompson model with Klein–Gordon non-locality (FMGT–KG) for analyzing Rayleigh wave behavior in a double-porous thermoelastic medium.

Methods

A modified nonlocal Fourier law is formulated to incorporate fractional memory effects and spatial nonlocality. The governing equations are developed within the FMGT–KG framework and solved using an eigenvalue approach. Frequency equations are derived for both isothermal and thermally insulated surface conditions.

Results

The proposed model enables the numerical prediction of key wave characteristics, including wave speed (V), specific loss (SL), penetration depth ( \(\delta\) ), and attenuation ( \(Q\) ). The results demonstrate the capability of the FMGT–KG framework to describe anomalous wave behavior more accurately than classical thermoelastic models.

Conclusion

The developed formulation provides a rigorous mathematical and physical framework for studying Rayleigh wave propagation in complex double-porous thermoelastic media. The findings are relevant to geophysical wave analysis, nondestructive material evaluation, and advanced modeling of dissipative wave phenomena.