Dispersion characteristics and mode conversion of guided waves in plate-like structures with arbitrarily varying thickness.

Understanding explicitly the dispersion and mode conversion of guided waves in plates with varying thickness is crucial for enhancing the accuracy of guided wave tomography. While prior studies have examined dispersion in such structures, a unified framework that links evolving dispersion characteristics and modal conversion with adiabatic wave theory for arbitrary thickness variations remains absent. In this study, we systematically analyse thickness-dependent dispersion in tapered, stepped, and arbitrarily varying plates using finite element (FE) simulation, semi-analytical finite element (SAFE) calculation, and experiment. Our results confirm that local frequency-thickness product (fd) governs dispersion, with higher-order guided wave modes emerging when fd exceeds each mode's cutoff. Symmetric thickness variations lead to intra-family conversions, while nonsymmetric configurations induce inter-family conversions. Moreover, we demonstrate that energy distribution among the converted guided wave modes strongly depends on the thickness gradient-gradual variations promote smooth, continuous energy transfer, whereas abrupt changes concentrate energy into fewer, higher-order modes. Finally, the introduction of a weighted time-distance mapping technique accurately compensates for dispersion effects, thereby validating our model. This work provides a solid foundation for future research on complex wave dynamics in structures with two-dimensional cross-sectional variations and advances guided wave tomography for engineering applications.