On Coupled Flexural and Torsional Oscillations of a Vibrating Beam Gyroscopic System
Bibliographic record
Abstract
Gyroscopes are commonly used to measure the angle of rotation and its rate of change in several critical systems like airplanes. Therefore, there is a never-ending desire for researchers to increase measurement precision of these devices. In order to achieve this goal, some new gyroscopes have been invented recently. Especially, advent of micro manufacturing has appeared some sophisticated to more pre´cised gyroscopic systems. The widely-used gyroscopes are vibrating beam gyroscopes; however they face a very important drawback, called cross-coupling error. In presence of the secondary base rotations, significant errors will be produced in measurement of the gyroscope output. In order to deal with this issue, this paper addresses a novel gyroscopic system, called rocking-mass gyroscope. It is consist of four beams attached to a rigid substrate, undergoing coupled flexural and torsional vibrations with a finite mass attached in the middle. This configuration is such that, it does not encounter the same problems as vibrating beam gyroscopes. This configuration makes the vibration analysis very complicated. Despite this fact, a thorough analysis is performed in this paper. Using Extended Hamilton’s principle, eight governing partial differential equations of motion along with their corresponding boundary conditions are derived. Further attempt is made to find the closed-form frequency equation of the system. Solving this equation needs high computational costs and gives the natural frequencies of the system. In spite of this fact, the system is analysed in the frequency domain using an exact method in full detail, for two cases of fixed and rotating base support. Furthermore, a detailed parameter sensitivity analysis is carried out to determine the effects of different parameters on the natural frequencies of the system. The contributions of this research are very important from two viewpoints. Firstly, determination of natural frequencies and resonance conditions are essential for design of the system, and design of appropriate control strategies. Secondly, frequency domain analysis forms the basis of time domain analysis, followed by exact mode superposition method.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".