Speed-dependent nonlinear broadband vibrations of smart functionally graded piezoelectric material plates
Bibliographic record
Abstract
In this work, speed-dependent nonlinear vibrations of functionally graded piezoelectric material plates are investigated both analytically and numerically. The functionally graded piezoelectric material plates move in the longitudinal direction at a constant speed. The material properties of functionally graded piezoelectric material plates have graded distribution in the thickness direction that obeys a power law. Adopting the Kármán nonlinear geometrical relations, the transverse equation of motion is derived from d’Alembert’s principle by considering the dynamic equilibrium relationships. After that, the Galerkin method is used to discretize the equation of motion, resulting in a set of ordinary differential equations with respect to time. These ordinary differential equations are solved analytically by utilizing the method of harmonic balance. Then, the approximate analytical results are validated by utilizing the adaptive step-size fourth-order Runge–Kutta technique. The stability of approximate analytical solutions is also examined via the perturbation method. Nonlinear frequency-amplitude characteristics show some interesting nonlinear vibration phenomena in the smart structures. Specially, the nonlinear broadband vibration is detected in the translational functionally graded piezoelectric material plates due to the mode interaction. Finally, a parametric study is conducted to reveal the effects of system parameters on the nonlinear vibration characteristics of the translational functionally graded piezoelectric material plates.
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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".