Reduced models for chaotic dynamics of a fluid-conveying pipe

Abstract

A high-dimensional model for chaotic vibration of a cantilever conveying fluid having an end-mass is investigated. The nonlinear partial differential equation describing the oscillations of the pipe is converted into a finite set of coupled nonlinear ordinary differential equation (ODEs) using a Galerkin projection with the uniform cantilever-beam modes as basis. Depending on the parameter range of interest, it turns out that the order of the coupled set of ODEs is much larger (up to 18 degree-of-freedom) in order to obtain a convergent solution. In order to construct a bifurcation diagram with the non-dimensional flow velocity as unfolding parameter, a prohibitive amount of computational effort is necessary in a single-processor (serial) personal computer. To alleviate this computational limitation, such bifurcation diagrams for high-order chaotic system are constructed in parallel computer simulation using multi-threading (i.e. auto-parallelism). A significant computational gain is achieved in terms of time-saving through parallel-processing. The computational gain permits a reliable construction of bifurcation diagrams in the chaotic regime within a reasonable time frame. Subsequently, the efficacy of a reduced-order model based on proper orthogonal mode (POD) is contrasted with the high-dimensional model (with uniform cantilever-beam mode as basis). Numerical results demonstrate the merits and drawbacks of the POD-based bifurcation diagram, depending on the non-dimensional flow-velocity chosen to construct the POD. Copyrigh