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.
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ASME 2006 Pressure Vessels and Piping/ICPVT-11 Conference
July 23–27, 2006
Vancouver, BC, Canada
Conference Sponsors:
- Pressure Vessels and Piping Division
ISBN:
0-7918-47888
PROCEEDINGS PAPER
Reduced Models for Chaotic Dynamics of a Fluid-Conveying Pipe
Abhijit Sarkar,
Abhijit Sarkar
Carleton University, Ottawa, ON, Canada
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Michael P. Paidoussis
Michael P. Paidoussis
McGill University, Montreal, QC, Canada
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Abhijit Sarkar
Carleton University, Ottawa, ON, Canada
Michael P. Paidoussis
McGill University, Montreal, QC, Canada
Paper No:
PVP2006-ICPVT-11-93944, pp. 795-804; 10 pages
Published Online:
July 23, 2008
Citation
Sarkar, A, & Paidoussis, MP. "Reduced Models for Chaotic Dynamics of a Fluid-Conveying Pipe." Proceedings of the ASME 2006 Pressure Vessels and Piping/ICPVT-11 Conference. Volume 9: 6th FSI, AE and FIV and N Symposium. Vancouver, BC, Canada. July 23–27, 2006. pp. 795-804. ASME. https://doi.org/10.1115/PVP2006-ICPVT-11-93944
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