Analytical and Spectral methods for Lamb wave simulations

Abstract

In applications where Lamb waves based damage detection methods are considered, conventional linear and quadratic finite elements commonly used to model elastic waves are inefficient. The required mesh to obtain relative accurate results derives in enormous computational cost when simulating the wave propagation behavior in time domain. Analytical methods offer fast and accurate results, but their application are limited to relatively simple geometries. To solve this problematic a hybrid analytic- spectral-element approach is developed here. Drawbacks of both formulations can be circumvented if we model the regions belonging to the plate geometry with analytical methods while the perturbations of the plate-like geometry are modeled using high-order (spectral) elements. This paper presents an efficient method to do the coupling. Using this hybrid formulation the numerical effort is reduced drastically. The functionality of the proposed scheme is shown studying the propagation of ultrasonic guided waves excited and received with piezoelectric transducers.