Nonlinear vibrations and dynamic stability of viscoelastic anisotropic fiber reinforced plates
Bibliographic record
Abstract
Fiber-reinforced plastic composites are one of the most widely used composite materials because they balance well between properties and cost. Despite their widespread use in the aviation and automotive industries, there is currently a lack of effective mathematical models for their calculation under various dynamic loads. The research object of this work is an anisotropic viscoelastic fiber-reinforced simply supported rectangular plate. Two dynamic problems are considered: vibrations of the plate under the influence of a uniformly distributed static load; stability of the plate compressed in one direction. Within the Kirchhoff–Love hypothesis framework, a mathematical model was built in a geometrically nonlinear formulation, taking into account the tangential forces of inertia. By the Bubnov–Galerkin method, based on a polynomial approximation of the deflection and displacement, the problem was reduced to solving systems of nonlinear ordinary integro-differential equations. With a weakly singular Koltunov–Rzhanitsyn kernel with variable coefficients, the resulting system was solved by a numerical method based on quadrature formulas. By using experimental studies, considering the directions of the fibers, the values of the rheological parameters of some plastic material (KAST-V and EDF) were obtained. The plate's dynamical behavior was investigated depending on the plate's geometric parameters and viscoelastic and inhomogeneous material properties. Results show the importance of taking into account the viscoelastic properties of the material when solving dynamic problems of anisotropic reinforced plates made of composite materials. In particular, when studying the problem of dynamic stability of an anisotropic reinforced plate made of KAST-V, the results obtained in elastic and viscoelastic formulations in some cases differ from each other by more than 20%.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| 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 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 source (direct Gemma or distilled Codex), 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".