Guided waves are now well established for some applications in the non-destructive evaluation of structures and offer potential for deployment in a vast array of other cases. For their development it is important to have reliable and accurate information about the modes that propagate for particular waveguide structures. Essential information that informs choices of mode transducer, operating frequencies and interpretation of signals, amongst other issues, is provided by the dispersion curves of different modes within various combinations of geometries and materials.In this paper a spectral collocation method is successfully used to handle the more complicated and realistic waveguide problems that are required in non-destructive evaluation; many pitfalls and limitations found in root-finding routines based on the partial wave method are overcome by using this approach. The general cases presented cover anisotropic homogeneous perfectly elastic materials in flat and cylindrical geometry. Non-destructive evaluation applications include complex waveguide structures, such as single or multi-layered fibre composites, lined, bonded and buried structures. For this reason, arbitrarily multi-layered systems with both solid and fluid layers are also addressed as well as the implementation of interface models of imperfect boundary conditions between layers.
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 growing use of composite materials for aerospace applications has resulted in a need for quantitative nondestructive evaluation (NDE) methods appropriate for characterizing damage in composite components. NDE simulation tools, such as ultrasound models, can aid in enabling optimized inspection methods and establishing confidence in inspection capabilities. In this paper a mathematical approach using the Lebedev Finite Difference (LFD) method is presented for ultrasonic wave simulation in composites. Boundary condition equations for implementing stress-free boundaries (necessary for simulation of NDE scenarios) are also presented. Quantitative comparisons between LFD guided wave ultrasound simulation results, experimental guided wave data, and dispersion curves are described. Additionally, stability tests are performed to establish the LFD code behavior in the presence of stress-free boundaries and low-symmetry anisotropy. Results show that LFD is an appropriate approach for simulating ultrasound in anisotropic composite materials and that the method is stable in the presence of low-symmetry anisotropy and stress-free boundaries. Studies presented in this paper include guided wave simulation in hexagonal, monoclinic, triclinic and layered composite laminates.
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