Nonlinear membrane stiffness model of a tennis racquet string bed
Bibliographic record
Abstract
The overall stiffness of the string bed of a tennis racquet depends on numerous factors including the size and shape of the string bed, initial string tension, string spacing, and string geometric and material properties. This article contributes an analytical model of the string bed that employs nonlinear membrane theory to estimate static stiffness. The partial differential equation governing string bed deformation is discretized using a one-term Galerkin approximation that employs a logarithmic shape function for the string bed deflection. The resulting force–displacement relation at the centre of the string bed yields the string bed stiffness as a function of the major design parameters, including the shape and size of the frame, string tension used during stringing, and string spacing, diameter, and elastic modulus. To assess the accuracy of this model, the predicted force–displacement relation was compared to that measured from experiments on a string bed instrumented with a load cell and photoelectric (laser) displacement sensor. Experimental results confirm that the analytical model yields accurate estimates of the string bed load–displacement characteristics, especially for displacements of 5 mm or less.
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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 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".