An HDST based XIGA Approach for Vibration Analysis of Cracked Bi-Directional Functionally Graded Plates

Abstract

Bi-directional functionally graded materials (BDFGMs), where properties vary in both in-plane and thickness directions, are increasingly used in aerospace components/structures to improve vibration performance through tailored stiffness and mass distribution. However, cracks inevitably develop during in-service conditions and can significantly influence their vibration behavior, making their consideration essential in vibration analysis and design. To address this, an extended isogeometric analysis (XIGA) in conjunction with higher-order shear deformation theory (HDST) is employed for the first time to investigate the vibration behavior of BDFG plates containing the through-the-thickness crack. HSDT naturally captures the shear deformation effect, whereas the NURBS basis functions of XIGA inherently satisfy the higher-order requirement of the HSDT plate kinematics. The materials are graded in two directions, and effective properties are obtained using the rule of mixtures. The proposed method is first validated against benchmark solutions for FGM plates with property variation only in the thickness direction. Subsequently, a parametric study is conducted to analyze the effects of crack length, orientation, boundary conditions, and material gradation on the natural frequencies and mode shapes. The results show excellent agreement with reference data and emphasize the critical role of both cracks and material gradation in the vibrational response. The developed HDST-XIGA framework offers a reliable and accurate tool for the dynamic analysis of BDFGMs.