Effect of material inhomogeneity on characteristics of a functionally graded hollow cylinder

Abstract

In this paper, we present a statement of the axisymmetric problem on steady-state oscillations of an inhomogeneous elastic cylinder on the basis of the general relations of the linear theory of elasticity. The material parameters and density are considered to be variable along the radial coordinate. The oscillations are caused by a distributed load applied to the outer part of the cylinder boundary. We reduce the direct problem on determination of the radial and longitudinal displacement components to the numerical solution of a number of canonical systems of differential equations with variable coefficients. On the basis of the solution obtained, we carry out the computational experiments to analyze the influence of the variable Lamé parameters on the displacement field components, the stress tensor components, the amplitude-frequency characteristics and the values of resonant frequencies.