Free Vibration Analysis of Laminated Composite Beams Considering Delamination Effects Using Generalized Lamination Theory

Laminated composites exhibit highly complex damage mechanisms. One of the most critical failure modes is delamination, which refers to the separation between adjacent layers and can lead to significant reductions in structural stiffness. A major challenge associated with delamination is its invisibility on the material surface, making visual detection difficult. Although vibration-based damage detection methods offer a promising solution for identifying delamination, the effectiveness of such approaches relies on the availability of an accurate numerical model that can capture the behavior of delaminated structures. This study focuses on the modeling of delamination damage in laminated composite beams and the investigation of their free vibration behavior through the generalized lamination theory and finite element analysis. The displacement field within each lamina is assumed to vary linearly based on Lagrange polynomials, while terms accounting for interlayer sliding and separation caused by delamination are explicitly included. The governing equations of motion are derived using Hamilton’s principle, and the corresponding mass and stiffness matrices are formulated using the Galerkin method. The influence of delamination length and position on the natural frequencies and mode shapes is examined under various boundary conditions and laminate stacking sequences. The results are compared with existing studies in the literature to validate the accuracy of the proposed model. Additionally, three-dimensional finite element models are developed using ANSYS® software to perform a comparative analysis. Two different modeling strategies for the delaminated interfaces are considered: in the first, nodes on the delaminated surfaces are allowed to move independently; in the second, contact elements are used to constrain the relative motion between layers. The impact of these two modeling approaches on the simulation results is evaluated in detail.