Wavefield analysis tools for wavenumber and velocities extraction in polar coordinates

Experimental characterization of Lamb waves in plate–like structures overcomes the intrinsic limits of a–priori Semi–Analytical Finite Elements simulations, where material inaccuracies and non–idealities can not be easily considered. Unfortunately, the experimental extraction of guided waves dispersion curves, and especially their polar representation along different directions of propagation at a given frequency, is not trivial. In non-isotropic materials, such analysis is a key aspect for a reliable and robust characterization of the waves behaviour. In this work, by exploiting Scanning Laser Doppler Vibrometer measurements with narrowband excitation, two different signal processing methods for the extraction of the wavenumber polar representation at the excitation frequency are investigated and characterized. The first method is based on a Distance Regularized Level Set algorithm, widely used in image processing and computer vision but, to the best of author’s knowledge, never used in the Lamb waves’ field. The second method is based on the two-dimensional sparse wavenumber analysis which exploits the wavefield sparse representation in the wavenumber domain. With a precise and reliable extraction of the wavenumber characteristic in the k–space, the polar representations at the excitation frequency of phase and group velocities can be estimated. The former, by exploiting the well-known wavenumber–frequency relation, the latter, instead, by computing numerical derivative among wavenumbers at multiple frequencies. The methodology has been validated on three different composite plates with different degrees of non-isotropy properties. The results show the effectiveness of the two methods, highlighting the advantages and disadvantages of both.