Effective stiffness matrix method for predicting the dispersion curves in general anisotropic composites

In multi-layered composite laminates, Lamb wave equations are obtained using the transfer matrix method and global matrix method. These methods have numerical issues (missing roots or spurious roots) while solving the Lamb wave equations especially at high frequencies and for the laminates with a large number of layers. In the present work, an effective stiffness matrix method (ESM) is presented to solve the Lamb wave equations without numerical issues. The proposed ESM method offers a simple and mathematically straightforward formulation as it considers the multi-layered laminate as a single homogenous layer with effective stiffness properties. The Lamb wave equations of a single monoclinic layer are first derived by considering the displacement field in three directions and solved for obtaining dispersion curves. The proposed ESM method is then applied to various laminate configurations to test the effectiveness of the method. The different laminate configurations include quasi-isotropic, cross-ply, generally anisotropic and orthotropic laminates. The efficacy of the proposed method is established in these cases. In addition, the directional dependency of Lamb wave propagation characteristic (wave velocity) with laminate configurations is evaluated and analysed.