An Investigation of the Aeroelastic Response of a Two-Dimensional, Structurally Nonlinear Airfoil Subject to External Excitation
Bibliographic record
Abstract
The results of an analytical investigation are presented for the aeroelastic response of a two-dimensional, structurally nonlinear airfoil subject to a forced excitation. The system is modeled as a two-dimensional, rigid airfoil section free to move in both the bending and pitching directions and possessing a rigid flap. The airfoil is mounted by torsional and translational springs attached at the elastic axis, and the flap motion is used to provide the forcing input to the system. The airfoil is immersed in an aerodynamic flow environment, modeled using incompressible thin airfoil theory for unsteady oscillatory motion. The equations of motion for the aeroelastic system are solved using a fourth-order Runge-Kutta numerical integration technique to provide time-history solutions of the response of the airfoil in the pitch and plunge directions. The time-histories are analysed using Fourier transform-based techniques to obtain frequency-domain response and transfer functions. Results show that the nonlinear response of the aeroelastic system contains frequencies other than the forcing frequency. When modal frequencies and damping values are calculated using standard Fourier-based techniques, it is shown that the super- and sub-harmonic frequency content in the nonlinear response can contribute to errors when results are compared to those obtained for the equivalent linear system. This paper describes an investigation of a method of analysis that, while based on the Fourier transform, has been modified to recognize and accommodate the nonlinear contribution to the system response. The method, developed by Bendat [1], uses a band-limited random input and separates the linear and nonlinear components of the response within the frequency domain. Results are given for the application of this method to the specific case of the structurally nonlinear aeroelastic system. It is shown that the method may be used to successfully recover the linear frequency response function using the input and output data for the nonlinear system.
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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 | 0.002 |
| 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 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 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".