The general problem of elastic wave propagation in multilayered anisotropic media

Abstract

Exact analytical treatment of the interaction of harmonic elastic waves with n-layered anisotropic plates is presented. Each layer of the plate can possess up to as low as monoclinic symmetry and thus allowing results for higher symmetry materials such as orthotropic, transversely isotropic, cubic, and isotropic to be obtained as special cases. The wave is allowed to propagate along an arbitrary angle from the normal to the plate as well as along any azimuthal angle. Solutions are obtained by using the transfer matrix method. According to this method formal solutions for each layer are derived and expressed in terms of wave amplitudes. By eliminating these amplitudes the stresses and displacements on one side of the layer are related to those of the other side. By satisfying appropriate continuity conditions at interlayer interfaces a global transfer matrix can be constructed which relates the displacements and stresses on one side of the plate to those on the other. Invoking appropriate boundary conditions on the plates outer boundaries a large variety of important problems can be solved. Of these mention is made of the propagation of free waves on the plate and the propagation of waves in a periodic media consisting of a periodic repetition of the plate. Confidence is the approach and results are confirmed by comparisons with whatever is available from specialized solutions. A variety of numerical illustrations are included.

Leaky Lamb Waves (LLW) in Multiorientation Composite Laminates

“…The leaky Lamb wave phenomenon has shown considerable potential as an NDE method [1]. Most results reported in this area to date have been concerned with unidirectional laminates [2][3][4]. This is attributed to the complexity involved in theoretically predicting the response of these materials, as well as to certain difficulties associated with the experimental research.…”

Lamb Wave Detection of Delaminations in Large Diameter Pipe Coatings

“…Assuming that the coatings are linear viscoelastic layers, for the time harmonic case, elastic and viscoelastic solutions are identical with the exception that the viscoelastic material constants are complex and frequency dependent [47]. By inserting the real and complex material parameters for the layers into the model through the transfer matrix method [38], the global matrix method [42], or a hybrid finite element-normal modes expansion method [43,45] we can obtain dispersion curves for the propagating Lamb wave modes. Through these methods it is apparent that there is the emergence of a decaying exponential term that causes attenuation of the propagating waves in the viscoelastic material due to the complex roots of the dispersion relations.…”

“…Xu and Datta showed that increased stiffness and increased density have similar effects of lowering the cutoff frequency of guided wave modes in a bonded plate [37]. In 1991 Nayfeh presented an exact analytical treatment of elastic wave propagation in multi-layered anisotropic media using the transfer matrix method, which derives the individual layer solutions as wave amplitudes, then eliminating these amplitudes relates the stresses and displacements on one side of the layer to the other [38]. Laperre and Thys showed experimentally and theoretically that Lamb mode coupling between and polymer coating and an aluminum plate makes the bilayer system switch between modes [39].…”

Dispersion loci of guided waves in viscoelastic composites of general anisotropy

“…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. More recently a Pseudospectral Collocation Method (PSCM) has been successfully used to find dispersion curves of guided waves in isotropic as well anisotropic elastic materials [9,10].…”