Modeling the dynamics of a vibrating string with a finite distributed unilateral constraint: Application to the sitar
Bibliographic record
Abstract
The free vibration response of an ideal string impacting a distributed parabolic obstacle located at its boundary has been analyzed, the goal being to understand and simulate a sitar string. The portion of the string in contact with the obstacle is governed by a different partial differential equation (PDE) from the free portion represented by the classical string equation. These two PDEs and corresponding boundary conditions, along with the transversality condition that governs the dynamics of the moving boundary, are obtained using Hamilton's principle. A Galerkin approximation is used to convert them into a system of nonlinear ordinary differential equations, with lower mode-shapes parametrized with respect to the location of the moving boundary as basis functions. This system is solved numerically and the behavior of the string studied from simulations. The advantages and disadvantages of the proposed method are discussed in comparison to the penalty approach for simulating wrapping contacts. Simulations with bridge-string parameters consistent with the configuration of a real sitar show that any degree of obstacle wrapping may occur during normal playing. Finally, the model is used to investigate the mechanism behind the generation of the buzzing tone in a sitar.
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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) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".