Elastic waves in free anisotropic plates

Abstract

The mathematical formalism for obtaining dispersion relations for acoustic waves in plates of arbitrary anisotropy is outlined, and dispersion curves for propagation in a (001)-cut cubic plate are presented. These results are compared to the uncoupled SV and P modes which, in turn, are related to the slowness curves for bulk waves. This approach provides an explanation for the behavior of the computed dispersion curves, and it also provides a means of approximating plate wave dispersion curves from the behavior of the slowness curves. The relationship of plate waves to surface waves is also explored for directions in which pseudosurface waves are known to propagate.

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

“…The fact that these dispersion relations cannot be further factorized has a physical interpretation as explained by Solie and Auld [26]: each dispersion relation is the determinant of the coefficient matrix of a set of equations whose unknowns are the amplitudes of the partial waves which give rise to the family of modes considered and the order of this non-reducible determinant is equal to the minimum number of partial waves needed for satisfying the boundary conditions. The six partial waves will be coupled by the boundary conditions and anisotropy of the crystal in various ways which depend on the problem under study.…”

Guided waves' dispersion curves in anisotropic viscoelastic single- and multi-layered media

“…The usage of dispersion curves for NDE is well established as the copious literature and studies on the subject show: analytical solutions using potentials or the partial wave decomposition for the isotropic plate and cylinder were found by Mindlin [1], Pao [2,3], Gazis [4] and Zemanek [5]. Studies and solutions for anisotropic media in flat, and in cylindrical, geometry are in Solie & Auld [6], Nayfeh & Chimenti [7] and, more recently, Li & Thompson [8] or Towfighi et al [9]. Also, attention has been given to multi-layer systems where fluid layers could also be present, such as fluid-filled pipes or plates surrounded by infinite fluid (or solid).…”

Dispersion loci of guided waves in viscoelastic composites of general anisotropy

“…The usage of dispersion curves for NDE is well established as the abundant literature and studies on the subject reflect: analytical solutions using potentials or the partial wave decomposition for the isotropic plate and cylinder were found by Mindlin [1] and Gazis [2] for instance. Solutions for anisotropic media in flat, and in cylindrical, geometry can be found in Solie and Auld [3], Nayfeh and Chimenti [4] and, more recently, Li and Thompson [5]. Other solutions based on the Transfer or Global Matrix method are in [6], [7] or [8] and references therein.…”