A Differential Transform Approach for Modal Analysis of Variable Thickness Two-directional FGM Circular Plates on Elastic Foundations

Based on the differential transformation method, a semi-analytical solution is developed for free vibration and modal stress analyses of variable thickness two-directional functionally graded circular plates with restrained edges, resting on elastic foundations. Variations of the material and geometry parameters are monitored by five distinct exponential functions. The presented non-dimensional solution covers complex combinations of the material properties, edge conditions, and parameters of the elastic foundation. Results reveal that by a proper adoption of the distribution of the material properties, a somewhat uniform strength may be attained for the cross sections without the need to change the geometric parameters of the plate.