Nonlinear Dynamics of Functionally Graded Material Plates Under Dynamic Liquid Load and with Longitudinal Speed
Bibliographic record
Abstract
This paper investigates the dynamics of functionally graded material (FGM) plates under dynamic liquid load and with longitudinal speed. The liquid is assumed to be ideal so that it is incompressible, inviscid and irrotational. Based on the D’Alembert’s principle, the mathematical model of the system is developed by taking into account geometrical and material nonlinearities as well as velocity potential and Bernoulli’s equation. The Galerkin method is employed to discretize the partial differential governing equation to a series of ordinary differential ones, which are then analyzed via the use of the method of harmonic balance. Analytical results are compared with numerical ones to validate the present method. The stability of the steady-state response is examined by means of the perturbation technique. Linear analysis of the system shows the possible appearance of internal resonance, and nonlinear frequency-response curves demonstrate strong hardening-spring property of the system. A modal interaction behavior through 1:1 internal resonance is detected; the behavior can happen in a wide domain of constituent volume fraction, which is a unique phenomenon in moving FGM plates compared with their metallic counterparts. Furthermore, results show the modal interaction can be easily evoked in the moving FGM plate under dynamic liquid load, even while the plate is subjected to minimal exciting force or large damping. In addition, influence of the plate location on nonlinear dynamics of the system is examined; results show the dynamic response of the plate will change considerably when the plate is near the container wall.
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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".