Vibration analysis of non-uniform porous beams with functionally graded porosity distribution
Bibliographic record
Abstract
In this paper, the effect of different profile variations on vibrational properties of non-uniform beams made of graded porous materials is studied. Timoshenko beam theory is used to present the mathematical formulation of the problem including shear deformation, rotary inertia, non-uniformity of the cross-section, and graded porosity of the beam material. Three different variations of porosities through the thickness direction are introduced. The beam is assumed with the clamped condition at both ends. To obtain a numerical solution, finite element formulations of the governing equations are presented. The non-uniform beam is approximated by another beam consisting of n elements with piecewise constant thickness to keep the volume and hence the total mass unchanged for each element. The beam response has been calculated for the first three modes of vibration. In each case, the results for different types of thickness variation and porosity distribution are compared with those obtained for a beam with uniform thickness. The effects of non-uniformity, taper parameters, and porosity distribution on the frequencies and mode shapes are investigated. It is observed that a considerable change in frequencies and mode shapes can be achieved by selection of different thickness variation and porosity distribution.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 |
| 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 | 0.000 |
| 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)
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".