Vibrations of cracked rectangular FGM thick plates

Accurate first-of-its-kind solutions of the free vibration characteristics of side-cracked rectangular functionally graded material (FGM) thick plates are reported. From a brief review summary of available shear deformable plate theories, the well-established Reddy third-order plate theory apropos to cracked FGM thick plates is utilized. A novel Ritz procedure is developed incorporating special admissible functions - appropriately named in this study as crack functions - that properly account for the stress singularity behaviors in the neighborhood of a crack tip, and that properly account for the discontinuities of displacements and slops across a crack. Material properties of the FGM plates are assumed to vary continuously in the thickness direction according to the Mori-Tanaka scheme or a simple power law. The proposed special admissible functions accelerate the convergence of the extensive non-dimensional frequency solutions summarized. The first known non-dimensional frequencies of simply-supported and cantilevered cracked aluminum (Al) and ceramic (zirconia (ZrO₂)) or alumina (Al₂O₃) FGM thick plates of moderate thickness ratio (side-length to plate thickness, b/h = 10) are accurately determined. The effects of the volume fraction in the modeling of material distribution in the thickness direction and of cracks with different lengths, locations and orientations on the non-dimensional frequencies are investigated.