An Application of Stiffness Matrix Method to Determining of Dispersion Curves for Arbitrary Composite Materials

Abstract

Nowadays multi-layered composite material is very often applied in different kind of structures, like aircrafts, boats or vehicles. Parts of structures, which are made of these materials, are significantly lighter in comparison with traditional materials, like aluminum or steel alloys. On the other hand, the process of damage creation and evolution in the case of composites is much more complex. Moreover, the damages, which are characteristic for multi-layered materials (matrix cracking, fibre breakage, delaminations), are very difficult to detect at early stage of creation. Hence, there is a need to develop the advanced methods to detect them without destroying tested composite element. One of them is based on analysis of elastic wave propagation through the composite structure. Unfortunately, elastic waves possess strongly dispersive character. Thus, it is necessary to determine dispersion curves for investigated material before the tests in order to appropriate interpretation of received dynamic response of structure. In the case of arbitrary composite materials, it is rather challenging task. In the present article the relatively new, analytical method is applied, namely stiffness matrix method. The fundamental assumptions and the theoretical formulation of this method are discussed. Next numerical examples are presented, namely the dispersion curves are determined for the single orthotropic lamina and multi-layered 'quasi-isotropic' composite plate. The studied plates are made of glass fibres and epoxy resin. In the case of single lamina, the dispersion curves are determined in the parallel, perpendicular and arbitrary direction of waves propagation with respect to the fibre direction. In the case of multilayered plates, the dispersion curves are computed for one arbitrary direction. Additionally, the phase and group velocities for fundamental modes and fixed excitation frequency are estimated in all directions of waves propagation.

Determination of Dispersion Curves for Composite Materials with the Use of Stiffness Matrix Method

“…Therefore, the main aim of this work is to estimate the dispersion curves for the composites, which consist of this kind of layer materials, namely fibers with epoxy resin (CFRP, Fibers T300, Matrix N5208) and aluminum alloy PA38. Moreover, the present work should be considered as the continuation of the previous studies (Barski and Pająk, 2016). In that paper the dispersion curves obtained for a single lamina and for a multilayered composite material with quasiisotropic mechanical properties are presented.…”