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

TL;DR

This paper introduces a novel computational approach combining generalized reduction and dual numbers to efficiently calculate Lamb wave velocities, significantly improving speed without losing accuracy.

Contribution

The paper presents a new solution strategy for quadratic eigenvalue problems that enhances the efficiency of Lamb wave velocity calculations in elastic media.

Findings

Doubles computational speed and efficiency

Maintains high accuracy in velocity calculations

Applicable to a wide frequency range

Abstract

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.