Lamb wave mode decomposition and reconstruction based on the viscoelastic propagation model

Abstract

The accurate information of Lamb wave packets, such as amplitude, time of flight, and waveform, are essential for damage detection and evaluation. Due to the dispersive, multimodal, and attenuative characteristics of Lamb waves propagating in viscoelastic media, the desired mode component is difficult to be extracted from response signals. To address this issue, a technique based on the viscoelastic propagation model of Lamb waves is proposed in this article. Different from the conventional frequency–wavenumber domain filtering, the proposed technique achieves mode extraction by estimating the parameters of the viscoelastic propagation model, that is, complex amplitude am( r, ω) and effective complex wavenumber ξm( ω). Benefiting from that, it enables to decompose and reconstruct the desired mode from spatial–temporal measurement data. First, the frequency-dependent effective complex wavenumbers are extracted using the matrix pencil method, where the real parts represent the dispersion and the imaginary parts represent the effective attenuation. After that, the complex amplitudes are obtained by solving linear least-square equations. Finally, the complex amplitude, effective complex wavenumber, and frequency range of the desired mode are picked out to reconstruct the mode component in the time domain. The finite element simulation and experimental results verify the effectiveness of our technique. Furthermore, the performance of the proposed technique in noisy circumstances is analyzed through synthetic signals, which shows a small reconstruction error and a good convergence.