Dispersion relations for composite structures. Part I. Basic assumptions and realtionships for monoclinic lamina
Marek Barski, Adam Stawiarski, Małgorzata Chwał
Quarterly No. 3, 2016 pages 125-131
DOI:
keywords: Lamb waves, composite materials, anisotropic layer, dispersion curves, phase velocity, group velocity
abstract Nowadays, the propagation of elastic waves, particularly Lamb waves, is very often used in detecting damages in different kinds of composite materials. These systems are known as structural health monitoring (SHM). However, the phenomenon of Lamb wave propagation is very complex, especially in the case of thin-walled composite structures. Generally, three types of Lamb waves are observed, namely: longitudinal or pressure waves (L), shear vertical (SV) and shear horizontal (SH). The phase and group velocities of the mentioned waves depend on the thickness of the structure and the frequency of the excited signal. This fact makes proper interpretation of the received dynamic response of the structure difficult or even impossible. Therefore, determining the appropriate dispersion curves for different materials is a very important issue. In the present review, the most commonly used analytical approaches for determining dispersion curves in the case of multilayered composite plates are presented. At the very beginning of this work the solution for single isotropic plates is presented. Next, the fundamental assumptions of the theoretical model, which describe the elastic wave propagation phenomenon in multilayered materials, are discussed. In the first part, the relationships describing the elastic wave propagation for single orthotropic lamina are presented. There are two studied cases: namely when the wave front of the elastic wave travels along the principal directions of the material and when the wave front of the elastic wave travels in any arbitrary direction.