Lamb mode conversion in a plate with a delamination

Abstract

A theoretical study of Lamb mode propagation through a part of a plate containing a finite-length, delamination parallel with the surface is presented. In the delamination boundary region, which is taken parallel with the free plate surface, noncontact boundary conditions are assumed. The calculation is based on a modal decomposition method. As a result of diffraction on a delamination the incident Lamb mode is efficiently converted into Lamb modes with wave numbers close to the wave number of incident mode. The transmission coefficient of a Rayleigh wave incident on a delamination located near the surface has an oscillating dependence on the delamination parameters and has a pronounced minimum where there is a strong conversion into transmitted Lamb modes. Inversely, using the method of phase conjugation, a proper incident Lamb mode combination can be efficiently converted into a single transmitted Lamb or Rayleigh wave.

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“…In Diligent et al (2002), an analytical model based on mode superposition for scattering problems in plates, and its application for predicting the reflection coefficient of Lamb waves from a through-thickness hole, is presented combined with FEM simulation of the scattering and also with experimental data. Other works based on modal decomposition relate the reflected and transmitted waves to the properties of specific types of flaws (Shkerdin and Glorieux 2004;Castaings et al 2002).…”

Interaction of lamb modes with delaminations in plates coated by highly absorbing materials

“…The method to calculate the transmitted and reflected acoustic field is based on an expansion of this field in the Lamb eigenmodes in the different parts of this composite plate and on the use of boundary conditions at the vertical planes z = 0 and z = L. Because this method is described in detail in [9] and [10] for the case of a stress-free delamination, here we give just a concise description of its generalization for slip delaminations.…”

“…The most general orthogonality condition, applicable to both absorbing and nonabsorbing plates, for the geometry of Fig. 1, is given by the Appendix in [9]:…”

“…Rokhlin studied Lamb mode diffraction on horizontal delaminations situated exactly in the middle of the plate [3]- [5]. The effect of mode conversion on a horizontal delamination in a multimode plate was theoretically studied, and it was shown that, depending on the delamination length, a considerable part of an incident Lamb mode (or Rayleigh wave) energy is converted into transmitted Lamb modes [9]. Horizontal delaminations are more likely to appear in composite layered plates in which the existence of stresses leads to a deterioration of the coupling between layers and to development of delaminations.…”

“…In [9] and [10], the mode conversion efficiency was calculated as the ratio between the energy flow of the converted Lamb mode and the energy flow of the Lamb mode incident on the delamination region. Taking into account that the energy flow of Lamb modes is not easy to measure, it can be more suitable to analyze the influence of delaminations on the normal displacement amplitude at the surfaces of a plate or a composite bilayer.…”