Imaging guided wave evolution using wavenumber-distance spectrogram

In time domain nonlinear wave propagation analyses, a time-frequency map, which is commonly known as a spectrogram, gives a 2D-image of the evolution of multiple frequency components, also known as harmonics, as time progresses. This is useful in terms of knowing where the specific frequency components are present and how they evolve with time. Drawing a parallel between the time domain and the spatial domain, we have created a wavenumber-distance (k − x) spectrogram. Using the k − x spectrogram, the evolution of the propagating ultrasonic guided wave modes in a waveguide can be observed in terms of wavenumber and propagation distance in the wave-vector direction. The evolution can be driven by a multitude of reasons such as structural discontinuity, material change, and tapered geometry, to name a few. Given the frequency dependent nature of ultrasonic guided waves, frequency tuning can be performed to arrive at the optimal representation of the structural feature using the k-x spectrogram. Moreover, based on the nature of excitation, it is possible to obtain different k − x spectrogram images for the same set of frequencies. We consider the k − x spectrogram as a significant development because this type of energy based 2D-imaging in the spatial domain has potential applications in macro-defect localization, analyzing guided waves in inhomogeneous geometries, as well as creating a fingerprint for a given spatial feature in a waveguide or the whole waveguide. In this work, we show some example applications for the k-x spectrogram, deriving waveguide specific images based on the artificially created features in the waveguide. All the simulations are done in the frequency domain using a commercially available finite element package.