Isogeometric finite element method for the dynamic analysis of functionally graded plates

This study investigated the free vibration behavior of functionally graded plates using iso-geometric finite element analysis (IGA). The effective material properties were estimated through the rule of mixtures, accounting for composition changes governed by a power law. To achieve this, an efficient computational framework based on IGA was developed, utilizing NURBS (Non-uniform Rational B-Spline) basis functions for structural discretization. The analysis focused on assessing the impact of geometry and material gradation parameters on the natural frequencies of square plates under various boundary conditions. Several numerical examples were presented to demonstrate the effectiveness of the proposed approach, and the results were validated by comparing them with other published models. The study covered both isotropic and functionally graded materials, specifically Al/Al2O3 and Al/ZrO2, to examine the variations in their natural frequency responses. The findings revealed a significant influence of boundary conditions on the frequency response of Al/Al2O3. The research thus provided important insights into the vibrational characteristics of different materials, considering various gradation schemes, geometrical modifications, and boundary conditions, offering valuable guidance for material selection in specific applications.