Exact Solution of the Oscillatory Behavior Under Axial Force of a Beam with a Concentrated Mass Within its Interval
Bibliographic record
Abstract
This article addresses the exact solution of free vibration of a beam with a concentrated mass within its intervals when the beam is subjected to axial loadings. This problem is frequently encountered in the design and modeling of resonant micro-sensors, where an exact model is required to calibrate the frequency output with a physical measurand. The significance of this approach is its ability to determine the exact mode shapes of vibration, which are necessary in the study of the time-domain response of sensors and determination of stability regions. The effects of the concentrated mass ratio, its location on the beam, and the applied axial force on the natural frequencies and the mode shapes of the resonant beam were studied in detail. The results of this study reveal how the mass ratio and location can change the sensitivity of the sensor to the input axial force. As an application of the presented approach, the modeling of a fabricated micro-electro-mechanical system (MEMS) has been discussed.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 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 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".