Nonlinear Stability of Circular Cylindrical Shells in Annular and Unbounded Axial Flow
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Bibliographic record
Abstract
The stability of circular cylindrical shells with supported ends in compressible, inviscid axial flow is investigated. Nonlinearities due to finite-amplitude shell motion are considered by using Donnell’s nonlinear shallow-shell theory; the effect of viscous structural damping is taken into account. Two different in-plane constraints are applied at the shell edges: zero axial force and zero axial displacement; the other boundary conditions are those for simply supported shells. Linear potential flow theory is applied to describe the fluid-structure interaction. Both annular and unbounded external flow are considered by using two different sets of boundary conditions for the flow beyond the shell length: (i) a flexible wall of infinite extent in the longitudinal direction, and (ii) rigid extensions of the shell (baffles). The system is discretized by the Galerkin method and is investigated by using a model involving seven degrees-of-freedom, allowing for traveling-wave response of the shell and shell axisymmetric contraction. Results for both annular and unbounded external flow show that the system loses stability by divergence through strongly subcritical bifurcations. Jumps to bifurcated states can occur well before the onset of instability predicted by linear theory, showing that a linear study of shell stability is not sufficient for engineering applications.
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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 |
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