  A new solution strategy for quadratic eigenvalue problems, and the
derivatives of the eigenvalues, is proposed, by combining the generalized
reduction method with dual numbers. To demonstrate the method, we use the
quadratic eigenvalue problem encountered in the semi-analytical finite element
method (SAFE) as a guiding example. The SAFE method is designed to calculate
the spectrum of Lamb wave phase, group and energy velocities in (visco)elastic
orthotropic media, over a wide frequency range. It was found that the new
approach essentially doubles the computational speed and efficiency, without
sacrificing accuracy.
