A simplest Approach for Plotting the Disperison Curves in a Layered Composite Material Using the Floquet-Bloch Boundary Condition.

Structural health monitoring via guided waves has been a major player in material inspection and damage identification, as they travel long distances with relatively low attenuation, holding valuable insight about the structural integrity of the material. Nevertheless, this method needs a pre-understanding of the dispersive nature of the waves in order for a prompt identification of any eventual damage in the structure, thus, the importance of solving the dispersion relation.

In the case of anisotropic materials, for example composites, many methods have been implemented for solving the dispersion curves and which are robust and require expertise and mathematical background to solve analytically, such as Transfer Matrix Method (TMM), Global Matrix Method (GMM), Stifness Matrix Method (SMM), and Semi-Analytical Finite Element method (SAFE).

In this regard, this study proposes a simplest approach using the Floquet-Bloch periodic condition, which reduces the propagation problem to a unit cell, that is the smallest repeated cell possible in the structure. In other words, it considers the propagation in the first Brillouin zone only as it captures the eigenfrequencies that correspond to specific wave number values and which represent the modes propagating in the structure. As a result, Lamb waves dispersion curves in a layered CFRP composite laminate will be plotted using the Floquet-Bloch periodicity, as well as an analysis of the displacement in each layer of the CFRP.