Vibration and radial wave propagation velocity in functionally graded thick hollow cylinder

Abstract

This article presents the analysis of functionally graded thick hollow cylinders under dynamic load. The functionally graded cylinder is assumed to be made of many subcylinders. Each subcylinder is considered as an isotropic layer. Material’s properties in each layer are constant and functionally graded properties are resulted by suitable arrangement of layers in multilayer cylinder. The properties are controlled by volume fraction that is an exponential function of radius. The shell is assumed to be in plane strain condition, and is subjected to axisymmetric dynamic loading. The Navier equation is solved by Galerkin finite element and Newmark methods. In each interface between two layers, stress and displacement continuity are satisfied. By using the fast Fourier transform (FFT), the time response is transfered to frequency domain and natural frequencies are illustrated. Then the dynamic behavior of functionally graded thick hollow cylinder is discussed. The radial wave propagation due to an internal pressure unloading is studied. The time history of radial stresses are discussed and the mean velocity of radial stress wave propagation for different exponent “ n” of functionally graded material (FGM) are determined. Finally the functionally graded cylinder is assumed to be isotropic and the results are compared with the analytical results.