Localization of Vibration Propagation in Two-Dimensional Systems With Multiple Substructural Modes
Bibliographic record
Abstract
Localization of vibration propagation in randomly disordered weakly coupled two-dimensional cantilever-mesh-spring arrays, in which multiple substructural modes are considered for each cantilever, is studied in this paper. A method of regular perturbation for a linear algebraic system is applied to determine the localization factors, which are defined in terms of the angles of orientation and characterize the average exponential rates of growth or decay of the amplitudes of vibration in the given directions. Iterative formulations are derived to determine the amplitudes of vibration of the cantilevers. In the diagonal directions, a transfer matrix formulation is obtained. For a given direction of orientation, the localization behavior is similar to that of a one-dimensional cantilever-spring-mesh chain. The effect of the stiffnesses and the disorder in the stiffnesses of the cantilevers on the localization behavior of the system is investigated.
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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 | 0.001 |
| 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 | 0.001 |
| 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 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".