Algorithms for a Layered Heterogeneous Plate Under Sliding and Loading Conditions with an AI-Based PINN Extension

This study examines the effect of material heterogeneities and other structural factors on the dispersion of shear waves across a composite structure via two algorithms. The resulting dispersion relation is sought analytically and further examined numerically through the first algorithm. In addition, the study establishes a sensitivity analysis algorithm using an absolute normalized sensitivity procedure within the low-frequency spectrum, revealing the most sensitive parameters governing the overall dynamic response of the structure. In particular, for the benchmark rigidity, density and thickness ratios, the phase speed of the first mode is lowered by the skin heterogeneity in all three profiles when the foundation and sliding parameters are absent, most strongly for the quadratic profile (Type II); in the presence of a soft foundation and a sliding interface, the dependence on the heterogeneity parameter is no longer monotone for the exponential and hyperbolic profiles. Increasing the foundational stiffness enhances wave dispersion in the composite plate, whereas increasing the sliding contact parameter decreases shear wave dispersion. Regarding parameter sensitivity, evaluated locally on the dispersion curve, the stiffness of the foundation is found to be the most sensitive parameter for all three heterogeneity profiles. Furthermore, the analytically derived dispersion relations and absolute normalized sensitivity algorithms proposed herein serve as a physics-based foundation for machine learning approaches—specifically for training data generation and feature importance calibration—in the inverse characterization of layered inhomogeneous structures. Finally, a surrogate-initialized physics-informed neural network (PINN) and a data-driven surrogate network are formulated and, for the benchmark case of homogeneous layers with perfect bonding and traction-free outer faces, where a closed-form relation exists, are checked mode by mode against the exact dispersion relation (mean absolute error in frequency: 2.4×10−6 for the PINN at five wavenumbers and 1.4×10−2 for the surrogate over 0≤K≤1). Their extension to heterogeneous, sliding and loaded configurations is not demonstrated here and is left for future work.