Vibration characteristics of bidirectional functionally graded curved structures with cracks and variable porosity

The free vibration analysis of a bidirectional functionally graded (2D-FG) curved structure with a through-thickness longitudinal central crack is performed in the current analysis. The model employs higher-order displacement theory for kinematics, taking into consideration both situations with even and uneven porosity. The three grading patterns-exponential, sigmoid and power law distributions are included to depict the material variation through the axial and thickness directions. Using Hamilton's principle, the governing equations of the porous FG structure are obtained and subsequently solved through the isoparametric finite element method (FEM). The sensitivity of the predicted results is proven through convergence, and accuracy is validated by comparing with published data. This study aims to calculate the natural frequencies for various geometrical configurations and to examine how the crack-to-length ratio, power-law exponents (n x , n z ), porosity index, aspect ratio, porosity distribution type (even or uneven), thickness ratio, curvature ratio, and boundary conditions influence the free vibration characteristics of the FG panel.