A vibrating sitar string: Modeling the 3D dynamics of a plucked string impacting a spatial obstacle with friction
Bibliographic record
Abstract
In some musical instruments of Indian origin, such as sitar, veena, or tambura, the string termination is a shallow curved (parabolic) bridge. The string is usually plucked obliquely and interacts with the bridge, thus producing a buzzing or ringing tone which is significantly different from stringed instruments with knife edge supports like guitar. The string is also not restricted to planar motion and friction between bridge and string plays an important role in damping the non-planar motion. A mathematical model is presented for simulating a 3D vibrating string as it impacts a curved obstacle with friction. The bridge is represented as a foundation model with nonlinear visco-elastic springs; multiple distributed spatial impacts occur between the bridge and string, however the locations of these are not known in advance so must be determined during the simulation. Galerkin approximation is used to reduce the partial differential equations of motion to a set of nonlinear ordinary differential equations. These equations have been solved numerically for different contact and friction conditions. Parametric studies show the effect of bridge geometry, impact damping, and friction on the bidirectional vibration behavior of the string subject to an oblique plucking idealized as an initial condition.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 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".