Stresses in thin, multi-layer pipes in large radial vibrations

Abstract

Free, large radial oscillations of multi-layered, thin, long, pipes are investigated using the theory of finite elastic deformations. The material of each layer is assumed to be homogeneous, isotropic, hyperelastic and incompressible. Closed form solutions are obtained for the nonlinear, ordinary differential equation governing the motion of the inner surface of the cylinder pipe. The motions of the other material points can then be obtained using the incompressibility condition. It is shown that radial stress is negligible throughout the thickness of the pipe. Tangential stress distributions at different times are given as a function of the radial distance for one, two and three layer pipes.