Full 3D dispersion curve solutions for guided waves in generally anisotropic media

• Published in: Journal of sound and vibration 2016-02, Vol.363, p.545-559
• Main Authors: Hernando Quintanilla, F., Lowe, M.J.S., Craster, R.V.
• Format: Article
• Language: English
• Subjects: Algorithms; Anisotropy; Attenuation; Dispersion (wave); Dispersion Curves; Generally Anisotropic Viscoelastic Media; Guided Waves; Mathematical models; Non-destructive Evaluation; Spectral Collocation Method; Symmetry; Three dimensional; Wave propagation
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/j.jsv.2015.10.017

Dispersion curves of guided waves provide valuable information about the physical and elastic properties of waves propagating within a given waveguide structure. Algorithms to accurately compute these curves are an essential tool for engineers working in non-destructive evaluation and for scientists studying wave phenomena. Dispersion curves are typically computed for low or zero attenuation and presented in two or three dimensional plots. The former do not always provide a clear and complete picture of the dispersion loci and the latter are very difficult to obtain when high values of attenuation are involved and arbitrary anisotropy is considered in single or multi-layered systems. As a consequence, drawing correct and reliable conclusions is a challenging task in the modern applications that often utilize multi-layered anisotropic viscoelastic materials. These challenges are overcome here by using a spectral collocation method (SCM) to robustly find dispersion curves in the most complicated cases of high attenuation and arbitrary anisotropy. Solutions are then plotted in three-dimensional frequency-complex wavenumber space, thus gaining much deeper insight into the nature of these problems. The cases studied range from classical examples, which validate this approach, to new ones involving materials up to the most general triclinic class for both flat and cylindrical geometry in multi-layered systems. The apparent crossing of modes within the same symmetry family in viscoelastic media is also explained and clarified by the results. Finally, the consequences of the centre of symmetry, present in every crystal class, on the solutions are discussed.