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math.NA2026
Computing critical velocities in waveguides via multiparameter eigenvalue problems
Hauke Gravenkamp, Xiang Liu
In waveguide dynamics and moving-load problems (e.g., high-speed trains), critical velocities indicate the onset of strong vibration amplification. In systems that are invariant in…
math.NA2024
A Sylvester equation approach for the computation of zero-group-velocity points in waveguides
Bor Plestenjak, Daniel A. Kiefer, Hauke Gravenkamp
Eigenvalues of parameter-dependent quadratic eigenvalue problems form eigencurves. The critical points on these curves, where the derivative vanishes, are of practical interest. A…