Dynamic response of a thick functionally graded material tube under a moving load

Abstract

An analysis for axisymmetric steady-state response of an arbitrarily thick, isotropic, and functionally graded circular cylindrical shell of infinite length subjected to an axially moving normal ring load is presented. The mechanical properties of the graded shell are assumed to vary smoothly and continuously with the change of volume concentrations of the constituting materials across the thickness of the shell according to a power law distribution. The problem solution is derived by using Fourier transformation with respect to a moving reference frame in conjunction with the T-matrix solution technique that involves a system global transfer matrix, formed by applying continuity of the displacement and stress components at the interfaces of neighbouring layers. The analytical results are illustrated with numerical examples in which a metal-ceramic functionally graded material (FGM) pipe, composed of aluminium and zirconia, is subjected to a normal ring load travelling along the tube at constant speed. Four types of pipes are configured, i.e. a ceramic-rich composition with the ceramic at the inner (or outer) interface, and also a metal-rich composition with the metal at the inner (or outer) interface of the pipe. The presented model is used to determine the critical velocity of the moving load as a function of shell thickness for the selected material compositional gradient profiles. The effects of load velocity and shell thickness on the basic dynamic field quantities such as the mid-plane radial displacement and hoop stress amplitude along the pipe axis are also evaluated and discussed. Moreover, the response curves for the FGM shells are compared with those of equivalent bi-laminate shells containing comparable total volume fractions of constituent materials. Limiting cases are considered and good agreements with the solutions available in the literature are obtained.