Simulating Active Vibration Attenuation in Underactuated Spatial Structures
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Bibliographic record
Abstract
The active optimal attenuation of vibrations in spatial structures, modeled by finite elements with a possibly large number of degrees of freedom, is considered. The problem is formulated as underactuated in modal space, such that the desired number of controlled modes may be greater than the number of independent discrete actuators. Consequently, modal variables are coupled via second-order nonholonomic constraints that impose limitations on the dynamically admissible trajectories that a given structure may undergo. The optimality equations for the problem with a quadratic performance index are derived in a compact form involving time derivatives of all modal variables and Lagrange multipliers, which are required to ensure that the constraints are satisfied. These equations are solved by applying symbolic differential operators. The procedure employs standard finite element and symbolic mathematical software to render the optimal actuation forces and trajectories of all controlled modes (or any selected degrees of freedom) to attenuate vibrations. For illustration the method, referred to as the constrained modal space optimal control, is used to synthesize the active controls and predict response of a mast structure.
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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 | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| 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 it