Dynamic Analysis of Cracked Functionally Graded Curved Panels with Porosity Variation

The present study investigates the free-vibration behaviour of cracked functionally graded material (FGM) curved panels, considering variable porosity and different material grading patterns. A higher-order displacement theory is utilized to develop the mathematical model, and the Galerkin weak formulation of the vibration problem is obtained using Hamilton's principle. The numerical solution is obtained through the isoparametric finite element method, and a customized computational code is developed to evaluate the natural frequencies of damaged FG structures. Three material grading patterns—exponential, sigmoid, and power-law distributions—are considered, along with both even and uneven porosity distributions through the thickness. The effects of several key parameters, including crack length ratio, porosity index, grading pattern, aspect ratio, thicknessto-length ratio, curvature ratio, power-law exponent, and boundary conditions, on the vibration characteristics of FG panels are systematically examined. The results demonstrate that porosity distribution, crack size, and material grading significantly influence the structure's natural frequencies, providing useful insights for the design and analysis of cracked porous FG curved panels.