Semi-analytical finite element framework for wave dispersion in solid–fluid–poroelastic multilayers

Guided ultrasonic waves are widely used to characterize layered elastic structures; however, accurately predicting wave dispersion in multilayers composed of coupled solid, fluid, and porous media remains challenging. These difficulties arise from strong material heterogeneity and the complex physics governing multiphase interfaces. This work introduces a unified semi-analytical finite element framework combined with perfectly matched layers for modelling guided wave dispersion in solid–fluid–porous layered waveguides. A key novelty lies in a porosity-weighted interfacial formulation that rigorously enforces traction continuity, solid displacement compatibility, pore pressure equilibrium, and fluid flux conservation, thereby enabling physically consistent coupling across multiphase interfaces. In addition, a unified mathematical formulation is shown to handle both finite and infinite porous domains without reformulation, allowing seamless treatment of bounded porous layers and unbounded fluid-saturated media. By reducing the full three-dimensional waveguide problem to a two-dimensional cross-sectional eigenvalue formulation, the proposed approach achieves high computational efficiency while retaining geometric generality. The framework is validated through comparisons with analytical solutions and experimental measurements on representative porous structures, including battery anodes and saturated sintered materials. The results demonstrate accurate prediction of dispersion characteristics and reveal complex wave–structure interactions in multilayered porous systems. This unified framework provides a versatile and reliable tool for ultrasonic characterization and the analysis of heterogeneous material systems.