Natural frequencies of 2D-FG beams with internal crack defects on Winkler-Pasternak elastic foundation using finite element technique

The study's contribution is to investigate the free vibration response of internal multi-cracks Euler-Bernoulli 2D-FG beam structures on Winkler-Pasternak elastic foundations while accounting for pinned-pinned boundary conditions. Unlike traditional approaches limited to concrete and its variants, two models are developed to characterize the effects of crack location and size within the cross-section of 2D-FG beams, enabling more precise and adaptable analysis. The governing equations are discretized using the h-finite element technique (h-FET), while material properties vary following a power-law distribution across the beam's thickness and width directions. The stiffness of the fractured structure is computed using the reduced cross-section of the 2D-FG beam. Conversely, the system is stiffened by the longitudinal dispersion of the Winkler-Pasternak foundation support. The numerical results are compared with the findings of previous studies in terms of dimensionless fundamental frequencies for the purpose of convergence research. Comprehensive case studies investigate the effects of the power-law index, crack depth and position, and foundation stiffness on the first three natural frequencies of 2D-FG beams. These results offer novel insights into the dynamic analysis of complex FG structures.