Efficient Perturbation Analysis of Lamb Wave Dispersion Curves

Lamb waves are frequently used in nondestructive evaluation and are proposed for structural health monitoring applications. While many numerical methods to obtain dispersion curves for Lamb waves have been developed and implemented, in general they are time consuming and do not lend themselves to analyses involving the perturbation of parameters such as the small thickness and wave speed changes caused by temperature variations. Presented here are two methods of approximating the solutions of the Rayleigh-Lamb equations under a small perturbation assumption. The first method is a gradient-based linear approximation to the Raleigh-Lamb equations, and the second is a linear approximation method based on a number of pre-computed solutions to the Rayleigh-Lamb equations. Also presented is a simple algorithm to efficiently compute Lamb wave dispersion curves, which is used to study the approximation methods.