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Accurate measurement of guided modes in a plate using a bidirectional approach
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View: Figures


Image of FIG. 1.

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FIG. 1.

(Color online) Illustration of the bidirectional probe consisting of one receiving array placed between two transmitting arrays denoted 1 and 2. The differences of propagation path between the th and the th receiver, located at and , are marked with thick lines.

Image of FIG. 2.

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FIG. 2.

(Color online) Experimental wavenumbers vs frequency (1) (squares) and (2) (circles) obtained for a 4 mm thick bone-mimicking plate covered by a 10 mm thick silicone layer (T1). The inclination of the probe with respect to the bone-mimicking surface is 2°. The black crosses represent the average of (1) and (2). The continuous lines represent the case of the probe parallel to the bone-mimicking surface, i.e.,  = 0°. The parallel case wavenumbers are transformed following Eq. (2) with  = +2° (dashed red lines) and −2° (dash dot blue lines).

Image of FIG. 3.

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FIG. 3.

(Color online) Variation, as a function of the angle of (i) the experimental values (1) (squares) and (2) (circles) together with the average value of (1) and (2) (crosses) and (ii) their corresponding predicted values using Eq. (2) (dashed lines) and Eq. (3) (continuous line) for three particular modes at fixed frequencies obtained with sample (T1), marked with a black circles on Fig. 2 : 0.5, 0.85, and 1.75 MHz.

Image of FIG. 4.

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FIG. 4.

(Color online) Same as Fig. 2 but for the 4 mm thick bone-mimicking plate covered by a 2 mm thick fat-mimicking layer (T2).


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Measuring guided wave propagation in long bones is of interest to the medical community. When an inclination exists between the probe and the tested specimen surface, a bias is introduced on the guided mode wavenumbers. The aim of this study was to generalize the bidirectional axial transmission technique initially developed for the first arriving signal. Validation tests were performed on academic materials such a bone-mimicking plate covered with either a silicon or fat-mimicking layer. For any inclination, the wavenumbers measured with the probe parallel to the waveguide surface can be obtained by averaging the wavenumbers measured in two opposite directions.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Accurate measurement of guided modes in a plate using a bidirectional approach