A quasi-two-dimensional finite element formulation for analysis of active-passive constrained layer beams
Bibliographic record
Abstract
Active-passive damping is getting more popular with designers because it combines the complementary passive and active features in the control of structural vibrations. The classical three-layer structure has a viscoelastic-layer sandwiched between the host beam and a piezoelectric-layer. The more prevalent assumptions for modeling the system are the use of Euler-Bernoulli beam theory for both the host beam and piezoelectric-layer, and Timoshenko beam theory for the viscoelastic-layer. The assumption that transverse displacement is constant through the thickness limits accuracy and applicability of the model. The current formulation expresses the through-the-thickness dependency of the field variables as polynomials while their span dependency across a finite element is cubically interpolated. The versatility of the formulation is demonstrated via static and dynamic studies of examples taken from the literature. A beam treated with active-passive damping is presented and examined. The constitutive relation of the viscoelastic layer is represented using fractional derivatives and the Grünwald approximation. The extended Hamilton's principle is used to derive the system governing equations which are integrated with the Newmark time-integration system.
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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) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| 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) | 0.001 | 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 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".