Vibrations of a 3-Dimensional piping system

This paper briefly presents the transfer-matrix method (TMM) for the vibration analysis of a 3-dimensional piping system. The transfer matrix of a curved pipe with fluid was derived based on the exact solution of the governing equations, where the axial deformability was also taken into account. Only the steady-state response for the case of harmonic excitations was analyzed. With the formulation of the transfer matrix for a straight pipe and for a curved pipe, a 3-dimensional complex piping system can be easily modeled. The inviscid fluid-dynamic forces were derived according to the plug-flow approximation and the slender-body theory. As shown in a numerical example of a 3-dimesional piping system the comparison of the transfer function obtained with the finite-element method (FEM) and the TMM is quite good. On the basis of a comparison of the experimental results and the results obtained with the TMM, the correctness of the method was confirmed. It was also shown that the TMM is significantly faster than the FEM. (C) 2007 Journal of Mechanical Engineering. All rights reserved.