Vibration analysis of a Timoshenko beam on a moving base
Bibliographic record
Abstract
In this paper free vibration of a Timoshenko beam with a tip payload, which is mounted on a cart (referred to as TBC) is studied. The cart (base) can only have lateral displacement and the tip payload has both mass and mass moment of inertia. The center of mass of the payload does not coincide with the point where the beam connects to the payload. Therefore, the tip of the beam is exposed to an extra bending moment due to the inertial force of the payload. By employing Hamilton’s principle, the governing equations of motion and the associated boundary conditions for the TBC are first derived and then transferred into dimensionless forms. By using these governing equations and their associated boundary conditions, the closed-form frequency equation (characteristic equation) of the TBC is derived. This closed-form frequency equation is validated both analytically and numerically. The closed-form expressions for the mode shapes of the TBC and their orthogonality are also presented. By using the closed-form characteristic equation, a sensitivity study is performed and the changes in the natural frequencies versus changes in the physical parameters are investigated. The results presented in this paper are valuable for precise dynamic modeling and model-based control of flexible mobile manipulators; a flexible mobile manipulator is a flexible link manipulator with a moving base.
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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 | 0.000 |
| 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".