Investigation of guided wave properties of anisotropic composite laminates using a semi-analytical finite element method

Composite materials have been widely used in various applications, and guided waves are often used as a non-destructive testing tool to inspect defects or damage in composite laminates which are assemblies of multiple composite layers. These can have anisotropic material properties and arbitrary fibre orientation such that the guided wave properties of Lamb and shear-horizontal modes are direction-dependent. The group velocity of each wave mode is therefore to be considered with a component parallel to the wave propagation direction and a component perpendicular to the wave propagation direction. In this article, a semi-analytical finite element method is developed to model composite laminates with arbitrary fibre orientation and anisotropic material properties in each layer. Galerkin's principle is used to derive the weak forms of the governing equations, and an energy velocity formulation is used to calculate the parallel and perpendicular energy velocities. The finite element solutions are compared with available analytical and numerical solutions in the literature for forward waves, and excellent agreement is demonstrated. On this basis, the guided wave properties of backward waves have also been investigated. It is well understood that in an isotropic plate, the energy velocity of a backward wave is directed opposite to the phase velocity. However, in a composite laminate, the energy velocity of a backward wave is normally not exactly opposed to (180 out of phase with) the phase velocity but exhibits a skew angle. The angular dependences of wave properties of the forward and backward waves are investigated in this article.