Nonlinear dynamics and stability of cantilevered shells containing flowing or quiescent fluid
Bibliographic record
Abstract
This thesis presents a theoretical study of the nonlinear dynamics and stability of cantilevered shells conveying incompressible fluid for the first time; the steady aspects of the fluid viscosity are examined. The large-amplitude vibrations of geometrically-imperfect cylindrical cantilevered tanks containing quiescent, dense fluid is also investigated. Additionally, qualitative experiments are performed.The nonlinearity is geometric and is related to the large deformations of the structure. The nonlinear model of the shell is based on the modified Flugge's shell theory. The fluid flow is assumed to be irrotational; thus, linearized potential flow theory is utilized to determine the unsteady fluid-dynamic forces, associated to shell motions. The fluid behaviour beyond the free end of the shell is described by an outflow model, which characterizes the fluid boundary condition at the free end of the shell. Upstream of the clamped end, however, it is assumed that the fluid remains unperturbed. The Fourier transform method is employed to solve the governing equations for the fluid.The steady viscosity-related forces (skin friction and pressurization) are obtained by using the time-mean Navier--Stokes equations and are modelled as initial loadings, pre-stressing the shell. The unsteady fluid-dynamic forces, then, act as additional loadings on this pre-stressed configuration. The extended Hamilton's principle is utilized to formulate the coupled fluid--structure system. The displacement components of the shell are expanded by using trigonometric functions for the circumferential direction and the cantilevered beam eigenfunctions for the longitudinal direction. Axisymmetric modes are successfully incorporated into the solution expansion based on a physical approximation. The system is discretized and the resulting coupled non-linear ODEs are integrated numerically. Results with flowing fluid indicate that the shell loses stability through a supercritical Hopf bifurcation, leading to flutter. In the case of external excitation of a shell partially-filled quiescent fluid and with geometric imperfections, the nonlinear behaviour is found to be generally of softening type. Comparison of the theoretical results with the existing experimental data shows good agreement. In the qualitative experiments performed, the shell oscillation amplitudes are measured for a few different flow velocities. It is observed that both amplitude and frequency of the shell motion increase with the flow velocity.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| 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 | 0.001 | 0.001 |
| 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".