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

Area of Science:

• Solid Mechanics
• Wave Propagation
• Computational Physics

Background:

• Dispersion curves in elastic waveguides can exhibit zero-group-velocity (ZGV) points where group velocity is zero and wavenumber is finite.
• ZGV points are significant for nondestructive testing and material characterization due to localized elastodynamic energy.
• Accurate prediction of ZGV points is essential for reliable structural analysis and defect detection.

Purpose of the Study:

• To model and compute zero-group-velocity (ZGV) resonances in anisotropic plates.
• To develop and present three novel numerical procedures for calculating ZGV points in arbitrary nondissipative elastic waveguides.
• To provide a robust computational framework for ZGV point analysis.

Main Methods:

• Modeling ZGV resonances in anisotropic plates by introducing an additional modal solution, leading to a two-parameter eigenvalue problem.
• Developing a globally convergent numerical method for finding all ZGV points, suitable for smaller-scale problems.
• Implementing a fast, locally convergent Newton-type iteration for general applicability, requiring initial guesses.
• Combining global and local convergence strategies into a hybrid method for large-scale problems without initial guesses.

Main Results:

• Successful modeling of ZGV resonances in anisotropic plates.
• Demonstration of three complementary numerical methods for ZGV point computation.
• Validation of algorithms implemented in the GEW ZGV computation software.
• Identification of a hybrid method that balances efficiency, applicability, and completeness for ZGV point detection.

Conclusions:

• The presented numerical methods effectively compute zero-group-velocity (ZGV) points in elastic waveguides.
• The developed algorithms offer versatile solutions for predicting ZGV points, catering to different problem sizes and requirements.
• Accurate ZGV point computation is vital for advancing applications in nondestructive testing and quantitative structural characterization.