Nonlinear Dynamics of a Translational FGM Plate with Strong Mode Interaction
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Bibliographic record
Abstract
This paper examines the nonlinear dynamics of a translational functionally graded material (FGM) plate. The plate is composed of nickel and stainless steel, and its property is graded in the thickness direction that obeys a power-law distribution. By adopting the Kármán nonlinear geometrical relations, the equation of motion is derived from the D’Alembert’s principle by considering the dynamic equilibrium relationships for the out-of-plane vibration of the plate. The equation of motion is discretized by using the Galerkin method and thus a series of ordinary differential equations with mode-coupling terms are obtained. These ordinary differential equations are then solved by utilizing the method of harmonic balance. The analytical results are verified by the adaptive step-size fourth-order Runge–Kutta technique. The stability analysis of analytical solutions is also carried out by introducing small perturbation for steady state solutions. Both natural frequency and nonlinear frequency-amplitude characteristics are presented. In the translational FGM plate, strong nonlinear mode interaction phenomenon has been detected. The nonlinear frequency response shows intensive hardening-spring characteristics. Moreover, various system parameters such as power-law distribution, translating speed of the plate, in-plane tension force, damping coefficient and external excitation amplitude are selected as the controlled variables to present parametric study. Their effects on the nonlinear dynamical response of the translational FGM plate are highlighted.
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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 | 0.001 |
| 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)
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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