Analysis of cracked skew sandwich plates with functionally graded porous cores under free vibration

This study investigates the vibration behavior of cracked skew sandwich plates with a porous functionally graded core, utilizing the extended finite element method (XFEM). The modeling approach is based on higher-order shear deformation theory to enhance the accuracy of vibrational analysis. The crack geometry and its location within the discretized plate domain are determined using the level set method, followed by applying enrichment functions to effectively capture displacement discontinuities. The displacement field is further refined through the partition of unity technique. Material gradation in the functionally graded core is modeled using a power-law distribution, ensuring a smooth variation of properties across the thickness. A custom MATLAB code has been developed to implement the proposed methodology, which is validated through a comparative study with existing reference results. Parametric analyses are carried out to explore the impact of key design variables, including layer thickness ratios, skew angles, crack sizes, porosity distributions in the FG core, gradient indices, and edge conditions. The findings offer valuable insights into the vibration response of cracked FG plates and contribute to the development of advanced vibration analysis methods for composite structural systems.