Computing zero-group-velocity points in anisotropic elastic waveguides: Globally and locally convergent methods

Abstract

Dispersion curves of elastic waveguides exhibit points where the group velocity vanishes while the wavenumber remains finite. These are the so-called zero-group-velocity (ZGV) points. As the elastodynamic energy at these points remains confined close to the source, they are of practical interest for nondestructive testing and quantitative characterization of structures. These applications rely on the correct prediction of the ZGV points. In this contribution, we first model the ZGV resonances in anisotropic plates based on the appearance of an additional modal solution. The resulting governing equation is interpreted as a two-parameter eigenvalue problem. Subsequently, we present three complementary numerical procedures capable of computing ZGV points in arbitrary nondissipative elastic waveguides in the conventional sense that their axial power flux vanishes. The first method is globally convergent and guarantees to find all ZGV points but can only be used for small problems. The second procedure is a very fast, generally-applicable, Newton-type iteration that is locally convergent and requires initial guesses. The third method combines both kinds of approaches and yields a procedure that is applicable to large problems, does not require initial guesses and is likely to find all ZGV points. The algorithms are implemented in "GEW ZGV computation" (doi: 10.5281/zenodo.7537442).

Added Appendices A, B and D. Some clarifications in the text

References in corpus (3)

• Non contact probing of interfacial stiffnesses between two plates by Zero-Group Velocity Lamb modes
• Laser-Excited Elastic Guided Waves Reveal the Complex Mechanics of Nanoporous Silicon
• Solving singular generalized eigenvalue problems. Part II: projection and augmentation

Cited by in corpus (9)

• Beating resonance patterns and extreme power flux skewing in anisotropic elastic plates
• Computation of leaky waves in layered structures coupled to unbounded media by exploiting multiparameter eigenvalue problems
• Viscoelastic dynamics of a soft strip subject to a large deformation
• A Sylvester equation approach for the computation of zero-group-velocity points in waveguides
• Electroelastic guided wave dispersion in piezoelectric plates: spectral methods and laser-ultrasound experiments
• Frequency domain laser ultrasound for inertial confinement fusion target wall thickness measurements
• An Efficient Learning Method to Connect Observables
• On properties and numerical computation of critical points of eigencurves of bivariate matrix pencils
• Fast recovery of parametric eigenvalues depending on several parameters and location of high order exceptional points