Spectral finite element analysis of the vibration of straight fluid-filled pipes with flanges

A spectral finite element formulation for the analysis of stationary vibration of straight fluid-filled pipes is introduced. Element formulations for flanges and rigid masses attached to the pipe are also presented. In the spectral finite element formulation, the base functions are frequency-dependent solutions to the local equations of motion. The formulation is valid for arbitrarily long pipes and losses may be distributed in the system and may vary with frequency. The solutions of the equations of motion are expressed in terms of exponential functions, describing propagation in the waveguide, together with corresponding cross-sectional mode shapes. These solutions are found by using an FE discretization of the cross-sectional motion. To increase the numerical efficiency, methods for using FE shape functions with higher order polynomials are developed. The numerical accuracy is investigated by comparisons with results achieved with an exact formulation. It is found that, for frequencies of interest in many engineering problems, pipes may be modelled by using only one element to describe the fluid motion. The vibrations of a simple pipe structure with an infinite pipe, a flange and a small rigid mass are calculated. Just below the cut-on frequency of a shell mode, the stiffness controlled shell mode and the rigid mass may resonate, resulting in high vibration levels concentrated near the mass. (C) 1997 Academic Press Limited.