Reliability analysis of pipe conveying fluid with stochastic structural and fluid parameters

In this article, Monte Carlo simulation method is used in conjunction with finite elements for probabilistic self-excited vibration and stability analyses of pipes conveying fluid. For fluid-structure interaction, Euler-Bernoulli beam model is used for analyzing pipe structure and plug flow model is used for representing internal fluid flow in the pipe. By considering structural and fluid parameters of the system as random fields, the governing deterministic partial differential equation (PDE) of continuous system is transformed into a stochastic PDE. The continuous random fields are discretized by mid-point and local average discretization methods. For self-excited vibration analysis, the complex-valued eigenvalue problem is solved for investigating the eigenvalues and critical eigenfrequencies. Consequently, using complex eigenfrequencies and divergence velocities for every realization, the statistical responses of stochastic problem are obtained as expected values, standard deviations, probability density functions, and the probability of divergence occurrence. Moreover, the randomness effects of fluid parameters on the system are compared to those of structural parameters.