Vibration Analysis of Beams Using Alternative Admissible Functions With Penalties
Bibliographic record
Abstract
Abstract Assumed mode methods are often used in vibrations analysis, where the choice of assumed mode affects the stability and useability of the method. System eigenfunctions are often used for these expansions, however a change in the boundary conditions usually results in a change in eigenfunction. This paper investigates the use of Alternative Admissible Functions (AAF) with penalties for the vibration analysis of an Euler-Bernoulli beam for different boundary conditions. A key advantage of the proposed approach is that the choice of AAF does not depend on the boundary conditions since the boundary conditions are modelled via penalty functions. The mathematical formulation of the system matrices, and the effect of beam geometry changes on the computed natural frequencies and modeshapes are presented. The computed natural frequencies and mode shapes show an excellent agreement when compared with closed-form Euler-Bernoulli beam values. The study reveals that with an increase in the stiffness of the beam, the values of the penalties need to be increased. The results of this study suggest that boundary conditions, as well as beam geometrical parameters should be considered when selecting appropriate values of the penalties.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 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".