Mode Count and Modal Density of Isotropic Circular Cylindrical Shells Using a Modified Wavenumber Space Integration Method
Bibliographic record
Abstract
A new method based on the wavenumber space integration algorithm is proposed in order to obtain mode count and modal density of circular cylindrical shells. Instead of the simplified equation of motion, the exact equation is applied in mode count calculations. Modal plots are changed significantly in the k-space when using the exact equation. Mode repetition in cylindrical shells is represented by additional mode count curves in the k-space. On the other hand, a novel technique is presented in order to implement boundary condition effects in mode count and modal density calculations. Integrating these two significant corrections, a modified wavenumber space integration (MWSI) method is developed. Mode count and modal densities of three shells with different geometrical and acoustical properties are obtained using the MWSI method and conventional WSI. Results are verified using the exact mode count calculations. Moreover, effects of geometrical properties are studied on mode count plots in the k-space. Modal densities are obtained for cylindrical shells of different lengths, radii, and thicknesses. Finally, modal densities of cylindrical shells are compared to flat plates of the same size and boundary condition. Interesting results are obtained which will contribute in calculation of acoustic radiation efficiency and sound transmission in cylindrical shells.
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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) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| 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) | 0.000 | 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".