Sensitivity Analysis of the Frequency Response of a Piecewise Linear System in a Frequency Island
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Bibliographic record
Abstract
In this paper, we analyze the frequency response of a piecewise linear suspension system. Dynamical characteristics of the suspension will suddenly change when its relative displacement exceeds a clearance. Piecewise linear characteristics occur, for example, wherever we use stoppers to prevent the system from excessive relative displacement. A modified averaging method is used to find the frequency response of the system to a harmonic base excitation. A frequency island is observed, which corresponds to large amplitude vibration for a certain range of system parameters. The island is an isolated region that cannot be reached by the variation of excitation frequency and depends upon initial conditions. On the frequency island, the isolator amplifies the amplitude of vibration rather than suppressing it. This will be dangerous in applications where stoppers are installed to ensure relative displacement is limited. The ranges of system parameters causing the frequency island are determined. The results obtained by an analytical method are verified using numerical simulation.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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 |
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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