Reduced Models for Chaotic Dynamics of a Fluid-Conveying Pipe
Bibliographic record
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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".