Nonlinear Vibration of Truncated Conical Shells: Donnell, Sanders and Nemeth Theories
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Bibliographic record
Abstract
Abstract Nonlinear free vibration of truncated conical shells has been investigated for three different shell theories; Donnell, Sanders and Nemeth to investigate the effect of their simplifying assumptions. The displacement field of a finite element model that was obtained from the exact solution of equilibrium equations of Sander’s improved first-approximation theory is used to define the nonlinear strain energy of conical shells. Employing generalized coordinates method the equations of motion are derived and subsequently the amplitude equation of nonlinear vibration of conical shells was developed. The amplitude equation is solved for multiple cases of isotropic materials. Linear and nonlinear free vibration results are validated against the existing studies in scientific literature and demonstrate good accordance. The validated model is used to investigate effects of different parameters including circumferential mode number, cone-half angle, length to radius ratio, thickness to radius ratio and boundary conditions for the nonlinear vibration of conical shells.
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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 it