Hyperchaotic Behaviour of Shells Subjected to Flow and External Force
Bibliographic record
Abstract
This study treats the nonlinear behaviour of cylindrical shells subjected to internal fluid flow and to an external periodic transverse point force. The shell is supported at both ends by axial and rotational springs capable of simulating boundary conditions ranging from clamped to simple supports. This complex boundary condition configuration is preferred in our analysis in order to be able to compare theoretical findings with water-tunnel experiments available in the literature. The external concentrated point force is applied at mid-length of the immersed shell structure acting in the radial direction and the excitation frequency values lie within the spectral neighbourhood of one of the shell’s lowest frequencies for different flow velocities. The structural model is based on the full nonlinear Donnell shell equations of motion including the effect of the in-plane inertia and accounting for geometric imperfections. The fluid is assumed to be incompressible and inviscid and the flow isentropic and irrotational; it is modelled using potential flow theory with the addition of unsteady viscous terms obtained from the time-averaged Navier-Stokes equations. The coupled system is discretized using a solution expansion based on trigonometric functions satisfying the shell boundary conditions exactly. Numerical results show the nonlinear response at different flow velocities for (i) a fixed excitation amplitude and variable excitation frequency, and (ii) fixed excitation frequency varying the excitation amplitude. Bifurcation diagrams of Poincare´ maps obtained from direct time integration are presented, as well as the maximum Lyapunov exponent, in order to classify the system dynamics. In particular, periodic, quasi-periodic, sub-harmonic and chaotic responses have been detected. The full spectrum of the Lyapunov exponents and the Lyapunov dimension have been calculated for the chaotic response; they reveal the occurrence of large-dimension hyperchaos.
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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".