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

Abstract

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 utilise 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.0 Accepted for publication in the Journal of Sound and Vibration,

The symmetry and coupling properties of solutions in general anisotropic multilayer waveguides

“…As explained above and in [37], since each subdeterminant is not further reducible, crossings amongst modes with the same parity do not occur. Although illustrated for a specific case, this can all be done for completely general anisotropy.…”

“…Both sets of solutions are then independent of each other, mutually orthogonal, and the dispersion curves present no crossings amongst modes of the same parity. When (3) has no parity, the dispersion determinant does not factorize and no crossings occur amongst the dispersion curves of the only family of modes, see [3,37] for details.…”

“…[1,2,[22][23][24][25][26]. The investigation of dispersion curves in anisotropic single-and multiple-layer waveguides in cylindrical geometry by means of various methods are in [14,[27][28][29][30][31][32][33][34][35][36][37][38].…”

Complex dispersion solutions for guided waves and properties of non-propagating waves in a piezoelectric spherical plate

“…An 14 studied the evanescent Lamb waves in the plates and revealed the advantages of identification and location of cracks by the evanescent waves. Using the spectral collocation method, Quintanilla et al 15 studied the propagation and evanescent waves in plates and cylinders and gave a full 3D dispersion curve. Chen et al 16 theoretically studied the shear horizontal (SH) waves in a piezoelectric plate of cubic crystals and presented the full spectrum.…”

ElasticMatrix: A MATLAB toolbox for anisotropic elastic wave propagation in layered media

“…This software has been in development since 1990 and is primarily focused on calculating the dispersion solutions for multi-layered structures. The Disperse software was originally based the partial-wave method, however, is currently being updated to use the spectral collocation method [12,13,14,15,16]. The main limitation with Disperse is that it is closed-source.…”