Vibration Analysis of Bi-Directional Heated Functionally Graded Circular Nanoplates With Variable Thickness Using Generalized Differential Quadrature Method Integrated With Parallel Computing

The computational efficiency of the numerical solutions for structural analysis is always a concern for researchers. In the present work, the author incorporated a parallel computing algorithm and MAPLE in MATLAB to investigate the axisymmetric vibrations of bi-directional functionally graded circular plates with variable thickness under a thermal environment. The adopted approach reduced the computational cost significantly while using the generalized differential quadrature method with Chebyshev-Gauss-Lobatto grid distribution. The material properties and temperature profile are assumed to vary in radial and thickness directions. The mechanical properties of the material are assumed to be temperature-dependent. Being functionally graded material, the contribution of the physical neural surface has also been included. The thickness of the plate is assumed to vary linearly and parabolically in the radial direction. The governing equations for the defined problem are deduced using Hamiton’s energy principle by employing Mindlin’s plate theory and Eringen’s nonlocal theory. Further, the modified boundary conditions are obtained for simply-supported and free peripheral conditions that include the size-dependency in the boundary conditions. These equations are discretized by the generalized differential quadrature method to compute the normalized value of the frequency parameter. Silicon nitride (Si 3 N 4 ) and aluminium alloy (6061-T6Al) are adopted as ceramic and metal, respectively. The inclusion of MAPLE and a parallel computing algorithm for symbolic computation has drastically reduced the computational cost of the analysis. The investigation of the effect of nonlocal parameter, nonuniformity parameters, graded indexes and temperature profile on the frequency parameter has also been presented.