Dynamic stability of a pipe conveying fluid with an uncertain computational model

Abstract : The deterministic stability analysis developed by Paidoussis and Issid (1974) is extended to the case for which there are model uncertainties induced by modeling errors in the computational model. The aim of this work is twofold: (1) to propose a probabilistic model for the fluid-structure interaction considering modeling errors and (2) to analyze the stability and reliability of the stochastic system. The Euler-Bernoulli beam model is used to model the pipe and the plug flow model is used to take into account the internal flow in the pipe. The resulting differential equation is discretized by means ofvthe finite element method and a reduced-order model is constructed from some eigenmodes of thevbeam. A probabilistic approach is used to model uncertainties. The proposed strategy takes into account global uncertainties related to the noninertial coupled fluid forces (related to damping and stiffness). The resulting random eigenvalue problem is used to analyze flutter and divergence unstable modes of the system for different values of the dimensionless flow speed.