Stability and response analysis of a pipe with internal flow analyzed with an uncertain computational model

Abstract

This paper treats the problem of pipes conveying fluid, which has several engineering applications, such as micro-systems and drill-string dynamics. The aim of this work is twofold: (1) propose a stochastic model for the fluid-structure interaction considering modeling errors and (2) analyze the stability of the stochastic system. The Euler-Bernoulli model is used to model the pipe and the plug flow model is used to take into account the presence of the internal flow. The resulting differential equation is discretized by means of the finite element method and a reduced-order model is constructed with the normal modes of the beam model. A variation of the nonparametric probabilistic approach is used to model uncertainties in the fluid-structure interaction, since this approach is able to take into account modeling errors. The numerical results show how the random response of the system changes for different levels of uncertainties. The probability of instability is also computed for different levels of uncertainties.