Buckling and Vibrations of Multi-directional Functionally Graded Circular Plate Resting on Elastic Foundation

Abstract

The present paper deals with the axisymmetric vibrations of multi-directional functionally graded circular plate under uniform in-plane loads resting on elastic foundation. The mechanical properties of the plate material are assumed to vary in both radial and transverse directions. Generalized differential quadrature method has been employed to obtain the frequency equations from the differential equation governing the motion of such simply supported plates. The effect of volume fraction index, in-plane force parameter, foundation parameter, heterogeneity parameter and density parameter has been studied on the natural frequencies of vibration. The critical buckling loads have been computed. Three-dimensional modes shapes for first three natural frequencies have been presented.