Ultrasonic transmission of longitudinal modes in miniaturized cylindrical waveguides
Bibliographic record
Abstract
This study investigates the transmission and reflection of axisymmetric longitudinal L(0,n) modes in miniaturized cylindrical waveguides. The theoretical framework developed herein focuses on the analysis of the propagation of longitudinal modes within a homogeneous, elastic, and isotropic cylindrical waveguide with a varying cross-section. The novelty of this paper is found in the energy calculations and the consideration of higher-order modes for accurately describing the transmission and reflection coefficients at waveguide transitions. A 2D axisymmetric Finite Element Method (FEM) is used to calculate these coefficients based on the modal energy of propagating modes across different frequencies. The influence of geometrical and material properties, along with modal density, is examined numerically. Results demonstrate that optimal transmission occurs when the wavenumber ratio of propagating modes in connected waveguides is an integer, leading to effective coupling. Experimental validation on steel rods with diameters from 4 mm to 0.8 mm shows strong agreement with numerical results. It is observed that the L(0,1) mode around 1 MHz is the most suitable mode for efficient transmission between the waveguides. In contrast, the higher-order modes (L(0,2) around 1.25 MHz, L(0,3) between 1.3 and 1.5 MHz, and L(0,4) from 2.25 MHz) exhibit weak or irregular transmission, with more pronounced reflection behaviors, indicating that they are not optimal for efficient transmission in this configuration. These findings underline the importance of an optimized geometric transition in enhancing the transmission efficiency in such miniaturized waveguides.
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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 | 0.001 |
| 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)
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".