SENSITIVITY TO DAMPING IN NONLINEAR DYNAMIC ANALYSIS
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Bibliographic record
Abstract
Exact response sensitivities are derived and calculated for nonlinear dynamic analysis with Rayleigh damping formulated in terms of the current tangent stiffness matrix.The derivations show that the third-order tensor formed by the derivative of the tangent stiffness matrix with respect to the displacement vector is required.That quantity is non-zero only for material models that feature nonlinearity in at least a portion of their stress-strain curve.Bilinear models do not have that characteristic.The Bouc-Wen material model is selected in this paper to verify the implementations.That model exhibits a smooth transition between the elastic and the yield state.In order to obtain correct response sensitivities, it is necessary to let the third-order tensor amend the coefficient matrix of the system of equations that produce the sensitivity results.This paper also presents exact response sensitivities for modal damping and Rayleigh damping with coefficients implicitly specified as a target damping at two natural frequencies.Eigenvalue derivatives are implemented in order to calculate results for those cases.The amendment of the coefficient matrix is then asymmetric.Examples are presented to show the sensitivity of the displacement response with respect to four groups of parameters: material properties, crosssection geometry, mass, and parameters of the damping model.
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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 | 0.004 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.011 |
| 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 | 0.001 |
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