Zahra Sharif-Khodaei

Dong Xiao, Zahra Sharif-Khodaei, M. H. Aliabadi

The Semi-Analytical Finite Element (SAFE) method is widely used for computing guided wave dispersion curves in waveguides of arbitrary cross-section. Accurate mode tracking across consecutive wavenumber steps remains challenging, particularly in mode veering regions where eigenvalues become nearly degenerate and eigenvectors vary rapidly. This work establishes a rigorous theoretical framework for mode tracking in single-parameter Hermitian eigenvalue problems arising from SAFE formulations. We derive an explicit expression for the eigenvector derivative, revealing its inverse dependence on the eigenvalue gap, and prove that for any wavenumber and mode there exists a sufficiently small step ensuring unambiguous identification via the Modal Assurance Criterion. For symmetry-protected crossings, the Wigner-von Neumann non-crossing rule guarantees bounded eigenvector derivatives and reliable tracking even with coarse sampling. For continuous symmetries leading to degenerate subspaces, we introduce a rotation-invariant subspace MAC that treats each degenerate pair as a single entity. Based on these insights, we propose an adaptive wavenumber sampling algorithm that automatically refines the discretization where the MAC separation falls below a tolerance, using a novel error indicator to quantify tracking confidence. Validation on symmetric and unsymmetric laminates, an L-shaped bar, and a steel pipe demonstrates robust tracking in veering regions with substantially fewer points than uniform sampling or continuation-based approaches, while comparisons with open-source codes SAFEDC and Dispersion Calculator confirm accuracy and efficiency. The framework provides both theoretical guarantees and practical tools for reliable dispersion curve computation.

Dong Xiao, Zahra Sharif-Khodaei, M. H. Aliabadi

Physics-guided approaches offer a promising path toward accurate and generalisable impact identification in composite structures, especially when experimental data are sparse. This paper presents a hybrid framework for impact localisation and force estimation in composite plates, combining a data-driven implementation of First-Order Shear Deformation Theory (FSDT) with machine learning and uncertainty quantification. The structural configuration and material properties are inferred from dispersion relations, while boundary conditions are identified via modal characteristics to construct a low-fidelity but physically consistent FSDT model. This model enables physics-informed data augmentation for extrapolative localisation using supervised learning. Simultaneously, an adaptive regularisation scheme derived from the same model improves the robustness of impact force reconstruction. The framework also accounts for uncertainty by propagating localisation uncertainty through the force estimation process, producing probabilistic outputs. Validation on composite plate experiments confirms the framework's accuracy, robustness, and efficiency in reducing dependence on large training datasets. The proposed method offers a scalable and transferable solution for impact monitoring and structural health management in composite aerostructures.