Effect of Geometric Imperfections on the Free Vibration Behavior of L-shaped Functionally Graded Beam with Cracks

In this study, the effects of cracks and geometric imperfections on the free vibration characteristics of L-shaped functionally graded beams are comprehensively investigated. The governing equations are established based on the Timoshenko beam theory and Hamilton’s principle. The cracks are modeled using massless rotating springs, and the material properties vary along the beam’s thickness direction. The free vibration frequencies of the system are obtained by using the differential quadrature method. The results are verified by comparing them with the findings in the existing literature. Additionally, the influence of deformation type, geometric imperfection mode, crack location, and crack depth on the frequency of L-shaped functionally graded beams are analyzed.