A B-spline Finite Element Method for Structural Damping Beam Vibration Problem
Bibliographic record
Abstract
Beam structures are widely applied in civil engineering, mechanical engineering, and architectural design. The beam vibration equation with damping terms can better describe the specific properties of beams. In this paper, the cubic B-spline finite element method is used to solve the vibration problems of damping beams with a firmly supported edge at both ends, a simply supported edge at both ends, and a firmly supported edge at the left end and a simply supported edge at the right end. Moreover, the treatment methods of B-spline basis functions in the finite element space when solving problems under different boundary conditions are presented. By discretizing both the first and second time derivatives via the central difference scheme, the fully discrete scheme is derived, and a detailed analysis of the error estimation is conducted. Finally, the effectiveness of this method is verified through numerical examples, and the theoretical results are tested.
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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 | 0.012 | 0.010 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.002 |
| 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".