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A new solution strategy for quadratic eigenvalue problems, and thederivatives of the eigenvalues, is proposed, by combining the generalizedreduction method with dual numbers. To demonstrate the method, we use thequadratic eigenvalue problem encountered in the semi-analytical finite elementmethod (SAFE) as a guiding example. The SAFE method is designed to calculatethe spectrum of Lamb wave phase, group and energy velocities in (visco)elasticorthotropic media, over a wide frequency range. It was found that the newapproach essentially doubles the computational speed and efficiency, withoutsacrificing accuracy.

Novel algorithm for the computation of group and energy velocities of Lamb waves