Modeling guided wave propagation in multi-layered anisotropic composite laminates by state-vector formalism and the Legendre polynomials

This research presents a numerical method to analyze the propagation characteristics of guided waves in multilayered anisotropic composite laminates. The dispersion equations were derived theoretically, while the displacement and stress components of each layer are expressed in the form of state vectors, by combining the state-vector formalism and the Legendre polynomials (SVF-LP). The displacement fields are fitted approximately by Legendre polynomials, and the system of linear equations are constructed by the orthogonal projection. The eigenvalue/eigenvector solution is established to compute the phase dispersion curves instead of solving the transcendental dispersion equations. This overcomes the problem of missing roots in traditional matrix method effectively. In order to verify the robustness of the SVF-LP, three cases of multi-layered laminates, formed by isotropic material, unidirectional carbon-fiber epoxy prepreg and fiber-metal laminate (GLARE 3-3/2) are investigated, respectively. The influences of fiber angle change and the stacking sequence are primarily analyzed, on the dispersion characteristics and the displacement and stress profiles. The matrix method is also carried out to compare the accuracy of this proposed method, which is done by the commercial software Disperse. Finally, the displacement and stress profiles of fundamental modes of the guided waves in an arbitrary lay-up quasi-isotropic plate at a given frequency is discussed in details.