Bifurcation Analysis of an Airfoil Containing a Cubic Structural Nonlinearity and Subjected to Two-Dimensional Incompressible Flow
Bibliographic record
Abstract
The objective of the present work is detail bifurcation analysis of an airfoil subjected to two-dimensional incompressible inviscid flow taking into account a cubic structural nonlinearity in the pitch direction. The integro-dierenti al aeroelastic equations of motion for the airfoil are reformulated into a system of six first-order autonomous ordinary dierential equations. The reformulated equations are then used for the bifurcation analysis of an airfoil with a cubic structural nonlinearity in the pitch direction. The equations are either integrated numerically using defect-controlled method or analyzed using collocation method via AUTO software package. Fixed-point solutions are calculated analytically, and bifurcation diagrams showing both stable and unstable limit cycle oscillation are obtained. The types of bifurcations are assessed by evaluating the Floquet multipliers. A period doubling route to chaos was detected, and mildly chaotic behavior in a narrow range of velocity was confirmed via the calculation of the Lyapunov exponents.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 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) | 0.001 | 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".