Analysis of Nonlinear Forced Vibrations of Shallow Shells With Cut-Outs by Using the R-Function Method
Bibliographic record
Abstract
Geometrically nonlinear forced vibrations of shells based on the domains with cut-outs are investigated. Classical nonlinear shallow-shell theories retaining in-plane inertia is used to calculate the strain energy; the shear deformation is neglected. A mesh-free technique based on classic approximate functions and the R-function theory is used to build the discrete model of the nonlinear vibrations. This allowed for constructing the sequences of admissible functions that satisfy given boundary conditions in domains with complex geometries. Shell displacements are expanded by using Chebyshev orthogonal polynomials. A two-step approach is implemented to solve the problem: first a linear analysis is conducted to identify natural frequencies and corresponding natural modes to be used in the second step as a basis for nonlinear displacements. The system of ordinary differential equations is obtained by using Lagrange approach on both steps. The convergence of the solution is studied by using different multimodal expansions. The pseudo-arclength continuation method and bifurcation analysis are used to study the nonlinear equations of motion. Numerical responses are obtained in the spectral neighbourhood of the lowest natural frequency. When possible, obtained results are compared to those available in the literature.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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".