Wave propagation analysis in a bonded transversely isotropic structure: an axisymmetric potential-based approach

Purpose This study presents a computational analysis of three-dimensional Rayleigh-type surface wave propagation in a layered structure comprising two perfectly bonded transversely isotropic (TI) media. The work aims to elucidate the effects of material anisotropy and elastic contrast on wave dispersion, with implications for geotechnical engineering, nondestructive evaluation and structural diagnostics. Design/methodology/approach A potential-based analytical formulation is developed to derive the governing equations for elastodynamic wave propagation in TI media. Through Helmholtz-type decomposition and the enforcement of boundary conditions at the traction-free surface and bonded interface, the dispersion relation is established. The model is implemented computationally and validated across several TI configurations. A comprehensive parametric study is performed by fixing the substrate as titanium and varying the upper layer among a set of practically relevant transversely isotropic materials. The resulting dispersion characteristics are examined numerically using phase velocity plots and modal analyses. Findings The computational results validate the proposed analytical framework against known isotropic and TI cases. Significant sensitivity of dispersion behavior to the anisotropic stiffness parameters of the upper layer is observed. Variations in phase velocity, mode separation and energy localization are highlighted as functions of shear modulus and material symmetry. The study identifies critical thresholds where wave behavior undergoes qualitative transitions, reinforcing the importance of anisotropy in surface wave analysis. Research limitations/implications The present analytical model assumes perfectly bonded interfaces and linear elastic, TI behavior, which may not fully capture complexities such as imperfect contacts, material damping or inelastic responses encountered in real-world systems. Viscoelasticity and multilayer interactions are not included in the current formulation. These simplifications, while necessary for analytical tractability, may limit direct applicability to certain geophysical or engineered materials. Nonetheless, the framework offers a rigorous baseline for understanding anisotropic wave dispersion and can be extended in future work to incorporate more realistic boundary conditions, attenuation mechanisms, and layered heterogeneities for enhanced modeling fidelity. Practical implications The developed analytical framework provides engineers and researchers with a robust tool to predict Rayleigh-type wave behavior in anisotropic layered systems, which are common in geotechnical structures, seismic zones and advanced composite materials. By capturing directional dispersion and material-specific wave characteristics, the model supports improved design and assessment of layered media in applications such as nondestructive evaluation, structural health monitoring, and seismic response analysis. The ability to systematically evaluate the influence of anisotropy and material contrast enhances diagnostic accuracy and supports the development of optimized sensing strategies in both civil and aerospace engineering contexts. Social implications Accurate modeling of surface wave propagation in anisotropic layered media has important societal benefits, particularly in the context of seismic hazard assessment, resilient infrastructure design and disaster preparedness. By improving the understanding of how complex subsurface materials influence wave behavior, this work supports safer urban planning and risk mitigation in earthquake-prone regions. Additionally, the methodology can enhance nondestructive testing practices used in civil infrastructure and aerospace industries, contributing to public safety and sustainability through early detection of structural issues. The research thus indirectly aids in protecting lives, reducing economic losses and supporting informed engineering decisions in critical sectors. Originality/value This work provides a comprehensive axisymmetric formulation for Rayleigh-type wave propagation in layered TI media, an area with limited prior treatment in the literature. The analytical–computational approach developed herein enables accurate modeling of guided surface waves in anisotropic structures. Its utility spans a range of engineering applications, including seismic exploration, nondestructive testing, aerospace composite evaluation and material-specific diagnostic modeling.