EFFECT OF GEOMETRIC NONLINEARITIES ON NONLINEAR VIBRATIONS OF CLOSED CYLINDRICAL SHELLS
Bibliographic record
Abstract
Geometrically nonlinear free vibrations of closed isotropic cylindrical shells are investigated through an analytical–numerical model. The method developed is a combination of Sanders–Koiter nonlinear shell theory and the finite element method. The cylindrical shell is subdivided into cylindrical finite elements and the displacement functions are derived from exact solutions of Sander's equations for thin cylindrical shells. Expressions for the mass, linear and nonlinear stiffness matrices are determined by exact analytical integration. Various boundary conditions of shell and in-plane effects are considered. Nonlinear responses are analyzed using the Runge–Kutta numerical method. The nonlinear frequency ratio is determined with respect to the amplitude thickness ratio of the motion for different study cases. Detailed numerical results are presented for various parameters for a closed isotropic shell, indicating either hardening or softening types of nonlinear behaviors, depending on the structure data. The present results show good agreement with the published ones for several cases of shells. This research clarifies the current disagreement about various types of cylindrical shells with geometric nonlinearities.
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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".