Modeling guided elastic waves in generally anisotropic media using a spectral collocation method

Abstract

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.

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

“…(7) after having recast them in matrix form, in the same fashion as was done for the equations of motion, this procedure is described in detail in [14].…”

“…A comprehensive description of the SCM is in [12], [14] and, with particular relevance to the present case, in [15]. The main idea behind the SCM is to convert the partial differential equations of the acoustic field into a generalized matrix eigenvalue problem whose eigenvalues are computed thus yielding the full spectrum.…”

“…This serves as a further validation of the SCM approach. A complete description of the validation of the SCM for the study of guided waves in anisotropic media, elastic and viscoelastic, is in [14] and, of particular importance to the present case, in [15]. Throughout this section the conventional non-dimensional axis convention is adopted for the three-dimensional plots.…”

“…In section 2 a very brief description of the SCM, and its implementation is given, this is kept to a minimum to avoid repetition and the reader is referred to [12], [14], [15] and references therein for all the details about the SCM scheme and an extensive discussion of its principal features when used to solve acoustic guided wave problems. Some modifications are required here and these are outlined.…”

“…More recently, one of these variants known as Spectral Collocation Method (SCM) has been successfully used to model guided waves in elastic and viscoelastic generally anisotropic media, [14] and [15] respectively.…”