Parameter Sensitivity Analysis of Rotating Beams in Frequency Domain
Bibliographic record
Abstract
Many mechanical rotating systems can be modeled as a cantilever beam attached to a rotating substrate. Vibratory beam gyroscopes are good examples of such systems. They consist of a rotating beam with a tip mass, attached to a rotating base. Due to the base rotation, the governing partial differential equations of the system are coupled, and hence, the system undergoes coupled torsional-bending vibrations. The coupling effect complicates the frequency analysis of the system, especially in determining the system characteristic equation. Many investigators have chosen to use the assumed mode method in their analysis of such systems instead of extracting the exact mode shapes of the system. In spite of all these difficulties, this paper addresses the exact frequency analysis of such systems and presents a closed-form frequency characteristic equation and evaluates the accurate values of the natural frequencies. The application of the proposed method is not limited to the system at hand, as it can be utilized for analyzing general systems with coupled governing equations of motion. Having analyzed a closed-form frequency equation has two valuable advantages: a) it can serve as the basis for the subsequent time-domain analysis; and b) it can be very essential in developing control strategies. In this study a thorough sensitivity analysis is performed to determine the effects of different parameters on the natural frequencies of the coupled vibrating system. The proposed method reveals some interesting findings in the systems which were difficult, if not impossible, to be revealed by the assumed mode method commonly utilized in many research work reported recently in literature.
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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 | 0.001 |
| 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 |
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".