Determination of group velocity of propagation of Lamb waves in aluminium plate using piezoelectric transducers

Abstract

A prior knowledge of group velocities of Lamb wave modes is a key for analysis of time signals in guidedwave based structural health monitoring. The identification of multiple wave modes may be complicated due to dependency of group velocity on frequency (dispersion). These dependencies for infinite plate of constant thickness can be calculated by a numerical solution of analytic equation. Two alternative approaches to determine group velocities of zero-order Lamb wave modes in aluminum plate were used in this work: Two-dimensional Fast Fourier Transform (2D-FFT) and methods of time-frequency processing. 2D-FFT requires a high number of time signals in equidistant points, therefore it was applied on data from finite element analysis of wave propagation in the plate. Group velocities for chosen frequencies were also determined using wavelet transform (WT) of signals as differencies of times of arrival measured by a pair of piezoelectric transducers. The results from 2D-FFT and wavelet transform were compared to the analytic solution.

UQ eSpace

“…The most cost-effective and convenient approach is typically FEM modelling due to several commercially available products such as ANSYS, ABAQUS and Patran [2]. As such, many authors have simulated Lamb waves using FEM in a wide range of studies (see Figure 6) [1,8,10,11,14,19,20,[26][27][28][29]. Su outlined the two main requirements for modelling Lamb waves via FEM; activation of the wave pulse and acquisition of the response [2].…”

“…Widening of the wave pulse is due to the dispersive relationship between velocity and frequency. This behaviour can make it difficult to identify the boundary of the wave envelope, which is usually defined by a certain cut off threshold, and can lead to complications when attempting to measure the time of arrival (ToA) of a signal [11,12,14]. The Rayleigh-Lamb equations describe the dispersive characteristics of Lamb waves [3].…”

“…Authors have shown it is possible to simulate Lamb waves in 2D and 3D FEM simulation environments. The typical element type used by most authors for 2D simulations is a 4-node quadrilateral structural element [10,14,19,28,29]. In ANSYS this element type is the PLANE42 2D Structural Solid, which assumes plane strain or plane stress and has a total of eight degrees of freedom (DOF) (each node is capable of translation in the x/y directions) [31,32].…”

“…Another signal processing tool commonly used to analyse Lamb waves is the 2-dimensional Fast Fourier Transform (2D FFT) [2,14,29,35,36]. Alleyne and Cawley investigated the 2D-FFT for measurement of propagating Lamb wave signals [35].…”

“…: Ng and Veidt used ANSYS to model the interaction between the A0 mode and a delamination in a carbon/epoxy composite plate (a) [8]. Lasˇova´ used ABAQUS to conduct a two-dimensional analysis of the propagation of the A0 and S0 modes in an aluminium plate [14].…”