Free Vibration Analysis of Non-Prismatic Beam under Clamped and Simply Supported Boundary Conditions
Bibliographic record
Abstract
Non-prismatic beams, which serve crucial roles in mechanical engineering applications, are subjected to both static and dynamic loads.Hence, their thorough analysisparticularly under free vibration-is of significant importance.This research undertakes an in-depth investigation into the free vibration characteristics of non-prismatic Euler-Bernoulli beams that exhibit linear variations in both width and height.These beams were studied under two distinct boundary conditions: simple support and clampedclamped scenarios.The study's approach was twofold: analytical and numerical.The analytical method entailed computing the equivalent area and the equivalent second moment of area, thereby enabling an exploration of how variations in the second moment of inertia and cross-sectional area affect the natural frequencies and mode shapes of non-prismatic beams.Conversely, the numerical method employed the finite element method through ANSYS APDL software (version 17.2).The study's findings revealed that as the height and width of the beam decrease, natural frequencies decline and the maximum amplitude of the mode shapes escalates.It should be noted that the rate of decrease is more pronounced with changes in height than with alterations in width.Furthermore, the diminishing rate of natural frequencies and the decreasing maximum amplitude of the mode shape became more pronounced with the increase in mode number when the beam's height and width decreased.The results derived from the analytical procedure were validated against those from finite element analysis and other literature sources, demonstrating the reliability of the current method.The proposed analytical methodology, in its simplicity of use and accuracy, demonstrates considerable promise in comparison to numerical results.
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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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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".