Dispersion relations for composite structures. Part II. Methods of determining dispersion curves
Marek Barski, Adam Stawiarski, Małgorzata Chwał
Quarterly No. 3, 2016 pages 147-153
DOI:
keywords: Lamb waves, composite materials, anisotropic layer, dispersion curves, phase velocity, group velocity
abstract In the first part of the current review, the fundamental assumptions of the theoretical model of elastic waves propagation in multilayered composite material are presented. Next, the equations which describe elastic wave motion in the case of single orthotropic lamina are derived. In the second part of this work, the most commonly used method of determining dispersion curves for multilayered composite material are discussed, namely: the transfer matrix method (TMM), global matrix method (GMM), stiffness matrix method (SMM) and finally the semi-analytical finite element method (SAFE). The first three methods are based on the relationships which are derived in the first part of this review. Moreover, TMM and GMM should be considered numerically unstable in the case of a relatively large product value of wave frequency and the total thickness of the composite plate. However, SMM seems to be unconditionally stable. The last method is based on the finite element approach and it can be used in order to confirm the results obtained using the analytical method. Finally, exemplary dispersion curves are presented. The dispersion curves are determined for the 8-th layer of the composite material, which is made of carbon fiber and epoxy resin. It is assumed that the wave front travels in an arbitrary direction.