Nonlinear dynamics of a hanging cantilevered pipe simultaneously subjected to internal and external axial flows
Bibliographic record
Abstract
A nonlinear model for the dynamics of a hanging cantilevered pipe simultaneously subjected to internal and external axial flows is developed in this paper. The pipe discharges fluid downwards, which then flows upwards through an annular region contained by a rigid channel. Thus, the external flow is dependent on the internal one, and confined over the whole length of the cantilever. A nonlinear equation of motion is derived for that system via Hamilton’s principle to third-order accuracy. The fluid-related forces associated with the external flow; namely the inviscid, hydrostatic and viscous forces are derived separately, as well as the non-conservative forces due to the internal flow. The equation of motion is nondimensionalized and then discretized utilizing Galerkin’s technique. The solution is obtained numerically and presented by means of bifurcation diagrams, time histories, power spectral density and phase-plane plots. The results are compared to those presented in experimental and linear theoretical studies from the literature having the same system parameters. It was found that the nonlinear theory can qualitatively predict the same dynamical behaviour as observed, and is in reasonable quantitative agreement with the recorded data. Moreover, this model provides a better estimation of the onset of instability compared to the linear one.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".