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Phase and group velocity measurement of ultrasonic guided wavetrains in plates by pulsed TV holography
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10.1121/1.3327795
/content/asa/journal/jasa/127/4/10.1121/1.3327795
http://aip.metastore.ingenta.com/content/asa/journal/jasa/127/4/10.1121/1.3327795

Figures

Image of FIG. 1.
FIG. 1.

Phase and group velocities of the and Lamb modes as a function of the frequency-thickness product for an aluminum plate having and . The continuous lines represent the phase velocity and the dashed lines stand for the group velocity. The four curves converge to the phase and group velocity of the non-dispersive Rayleigh wave.

Image of FIG. 2.
FIG. 2.

Layout of the experimental system.

Image of FIG. 3.
FIG. 3.

Maps corresponding to the out-of-plane displacement field of the surface points of a plate 1.51 mm thick produced by a wavetrain, consisting of 5 temporal cycles with a central frequency of 0.909 MHz at a given instant . (a) Instantaneous optical phase-change , which is proportional to the instantaneous out-of-plane displacement. (b) Modulus of the instantaneous complex optical phase-change , which is proportional to the instantaneous acoustic amplitude. (c) Phase of the instantaneous complex optical phase-change , which is equal to the instantaneous acoustic phase. (d) Instantaneous filtered optical phase-change . The actual size of the field of view is

Image of FIG. 4.
FIG. 4.

Profiles of the maps of Fig. 3 along the horizontal pixel row corresponding to the vertical coordinate in which the acoustic amplitude is maximum. (a) Profile of Fig. 3(d) (continuous line) along with the envelope (dashed line), which is obtained from Fig. 3(b). The Gaussian curve that best fits the envelope is also shown (continuous line). (b) Profile of Fig. 3(c).

Image of FIG. 5.
FIG. 5.

Maps of the instantaneous filtered optical phase-change , corresponding to four wavetrains showing different dispersive behaviors. The maps show three different instants of propagation around an arbitrary time instant . The dot marks the envelope peak, while the cross marks a point with a given value of the phase. (a) Rayleigh wavetrain in an aluminum slab 30.0 mm thick, consisting of 5 temporal cycles with a central frequency of 1.000 MHz. The actual size of the field of view is and . (b) wavetrain in an aluminum plate 1.97 mm thick, consisting of 5 temporal cycles with a central frequency of 0.714 MHz. The actual size of the field of view is and . (c) wavetrain in an aluminum plate 1.51 mm thick, consisting of 5 temporal cycles with a central frequency of 0.909 MHz. The actual size of the field of view is and . (d) wavetrain in an aluminum plate 2.98 mm thick, consisting of 10 temporal cycles with a central frequency of 0.870 MHz. The actual size of the field of view is and .

Image of FIG. 6.
FIG. 6.

Measured positions of the envelope peak (dots) and of a point with a given value of the phase (crosses) vs. time. The envelope peak is taken at the center of the Gaussian curve that best fits the envelope in a horizontal pixel row, as shown in Fig. 4(a). The constant phase point is taken in the same row, in particular, we consider a point where a transition in the phase between and takes place, and is located within the region in which the amplitude is larger than half its maximum value. (a) Rayleigh wavetrain in Fig. 5(a). (b) wavetrain in Fig. 5(b). (c) wavetrain in Fig. 5(c). (d) wavetrain in Fig. 5(d). For the sake of clarity, in (a), the points of a given value of the phase are vertically shifted 5 mm, and in (a), (b), and (d), only one out of two consecutive points is represented [all the points are represented in (c) as the number of maps in the corresponding sequence is much lower than in the other cases].

Tables

Generic image for table
TABLE I.

Experimental values of the phase and group velocities measured from the movies for the four modes considered in the experiment. The reference values of the theoretical phase and group velocities are also displayed.

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/content/asa/journal/jasa/127/4/10.1121/1.3327795
2010-04-05
2014-04-25
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Phase and group velocity measurement of ultrasonic guided wavetrains in plates by pulsed TV holography
http://aip.metastore.ingenta.com/content/asa/journal/jasa/127/4/10.1121/1.3327795
10.1121/1.3327795
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