Stability, Bifurcation and Jumping Phenomenon in a 2-D Model of Supersonic Lifting Surfaces
Bibliographic record
Abstract
This paper is concerned with the linear/nonlinear aeroelastic control of 2-D supersonic lifting surfaces. Its goal is to provide the feedback control mechanism enabling one to enlarge the flight envelope by increasing the flutter speed, and also to control the character, benign/catastrophic of the flutter instability boundary. Structural and aerodynamic nonlinearities are included in the aeroelastic governing equations, and linear and nonlinear feedback controls in both plunging and pitching are employed in conjunction with proportional velocity feedback controls. The attention of the paper is focused on multiple Hopf bifurcations. In particular, the jumping phenomenon found in our previous work will be further investigated to reveal the physical implications. It is found that such a jumping occurs when the system has multiple families of limit cycles bifurcating from a same set of parameter values with multiple solutions for frequencies. The case investigated in this paper is restricted to zero structure damping. Center manifold reduction and normal form theory are applied to consider the stability of post-flutter solutions and the associated jumping phenomenon. Numerical simulations are presented to show the implications of time delay in the considered controls.
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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".