AI Insight
This paper introduces a material homotopy continuation framework for computing dispersion curves in viscoelastic waveguides with arbitrary cross-sections. The method continuously transforms a lossy (viscoelastic) eigenvalue problem into a simpler lossless (elastic) one using an attenuation parameter, guaranteeing that mode identities tracked at the elastic stage remain valid at the viscoelastic stage without additional post-processing, provided no exceptional points are crossed along the parameter path. Validation across symmetric and unsymmetric laminates at various loss factors demonstrates both robustness and numerical accuracy, with diagnostic tools provided to detect potential mode-labeling errors in challenging high-loss cases.
Why it matters
Accurate and automated dispersion curve computation is critical for non-destructive testing, structural health monitoring, and the design of acoustic and ultrasonic waveguide-based devices, where material damping is unavoidable. This framework reduces the manual intervention currently required to track modes in lossy systems, potentially accelerating simulation workflows in aerospace, civil, and biomedical engineering applications.
arXiv:2605.15089v1 Announce Type: cross
Abstract: This paper presents the first systematic application of a material homotopy continuation framework for efficient, automated computation of dispersion curves in viscoelastic waveguides of arbitrary cross-section. A material homotopy continuously maps the original lossy problem to an auxiliary lossless one via an attenuation parameter s in [0,1], addressing the core challenges of the non-Hermitian eigenvalue problem. Grounded in analytic perturbation theory, the method guarantees branch identity continuity–a one-to-one correspondence between solutions at s=0 and s=1–provided the real-parameter path does not cross any exceptional points. Under a Type I exceptional point topology, physical mode labels established at the elastic stage remain valid at the viscoelastic stage without post-processing, yielding the characteristic real-part veering with imaginary-part crossing. The decoupling strategy performs reliable mode tracking in the Hermitian regime via adaptive wavenumber refinement, then propagates a sparse set of key solutions to the target viscoelastic state through predictor-corrector homotopy continuation. Numerical examples across symmetric and unsymmetric laminates validate the framework’s robustness and efficiency, with the majority of cases verified at a loss factor of approximately 0.003 and a single symmetric laminate providing additional support at 0.02. For a challenging unsymmetric laminate at a loss factor of 0.05, the method still produces numerically accurate solutions; two complementary diagnostic signatures–an extremely sharp imaginary-part crossing and a discernible discrepancy between spectral group velocity and energy flux velocity–warn of potential label mismatch and guide further analysis.