Supersonic Flutter of a Spherical Shell Partially Filled with Fluid
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Bibliographic record
Abstract
In the present study, a hybrid ?nite element method is applied to investigate the dynamic behavior of a spherical shell partially filled with fluid and subjected to external supersonic airflow. The structural formulation is a combination of linear spherical shell theory and the classic finite element method. In this hybrid method, the nodal displacements are derived from exact solution of spherical shell theory rather than approximated by polynomial functions. Therefore, the number of elements is a function of the complexity of the structure and it is not necessary to take a large number of elements to get rapid convergence. Linearized first-order potential (piston) theory with the curvature correction term is coupled with the structural model to account for aerodynamic loading. It is assumed that the fluid is incompressible and has no free surface effect. Fluid is considered as a velocity potential at each node of the shell element where its motion is expressed in terms of nodal elastic displacements at the ?uid-structure interface. Numerical simulation is done and vibration frequencies are obtained. The results are validated using numerical and theoretical data available in literature. The investigation is carried out for spherical shells with different boundary conditions, geometries, filling ratios, flow parameters, and radius to thickness ratios. Results show that the spherical shell loses its stability through coupled-mode flutter. This proposed hybrid finite element method can be used efficiently for analyzing the flutter of spherical shells employed in aerospace structures at less computational cost than other commercial FEM software.
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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