Imaging guided wave evolution using wavenumber-distance spectrogram

Anurup Guha, Cliff Lissenden

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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.

Original languageEnglish (US)
Title of host publicationHealth Monitoring of Structural and Biological Systems XV
EditorsPaul Fromme, Zhongqing Su
ISBN (Electronic)9781510640153
StatePublished - 2021
EventHealth Monitoring of Structural and Biological Systems XV 2021 - Virtual, Online, United States
Duration: Mar 22 2021Mar 26 2021

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
ISSN (Print)0277-786X
ISSN (Electronic)1996-756X


ConferenceHealth Monitoring of Structural and Biological Systems XV 2021
Country/TerritoryUnited States
CityVirtual, Online

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering


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