Subharmonic and superharmonic resonances of five-layered porous functionally graded sandwich cylindrical shells with two-layered viscoelastic cores
Bibliographic record
Abstract
In this research, the subharmonic (SUBH) and superharmonic (SUPH) resonances of five-layered porous functionally graded sandwich (PFGS) cylindrical shells with two-layered viscoelastic cores (VECs) are investigated. The sandwich cylindrical shell is composed of three porous functionally graded (PFG) face layers and two VECs. The VECs are made of Kelvin–Voigt type material. The material properties of the PFG face layers are considered as continuous through the thickness of each face regarding a porosity coefficient and a volume fraction index. Two types of five-layered PFGS cylindrical shells with two-layered VESs, including porosity evenly distributed (Type 1) and porosity unevenly distributed (Type 2) along the thickness direction, are considered in this research. Based on the Donnell shell theory, von-Kármán equation, and Hooke’s law, the stress-strain relations are developed for the five-layered PFGS cylindrical shells. The discretized governing equation via Galerkin’s method is also derived. With the governing equations proposed and the method of multiple scales, the SUBH and SUPH resonances of the shells are investigated systematically. The influences of geometrical, and material parameters on the SUBH and SUPH resonances of the system are studied and presented. New results for SUBH and SUPH resonances of the five-layered PFGS cylindrical shells with two-layered VECs are provided for the first time and can be utilized as a benchmark for researchers and engineers in this area.
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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 | 0.001 |
| 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".