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Guided wave propagation in single and double layer hollow cylinders embedded in infinite media
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10.1121/1.3531807
/content/asa/journal/jasa/129/2/10.1121/1.3531807
http://aip.metastore.ingenta.com/content/asa/journal/jasa/129/2/10.1121/1.3531807

Figures

Image of FIG. 1.
FIG. 1.

(Color online) A plot of a hollow cylinder with both finite elements and infinite elements, the pole is located at the center of the cross-section circle of the hollow cylinder.

Image of FIG. 2.
FIG. 2.

Illustration of (a) an infinite element, the distance between nodes 1 and 2 must be equal to the distance between node 1 and the pole, (b) nodes in mapped s space, node 1 located at s = −1, node 2 located at s = 0, and infinity in r space corresponding to s = +1, quadratic interpolation used for the infinite element.

Image of FIG. 3.
FIG. 3.

(Color online) Cross-section of a hollow cylinder with infinite media, finite soil layer between two layers to guarantee the continuity, (a) without viscoelastic coating and (b) with viscoelastic coating.

Image of FIG. 4.
FIG. 4.

(Color online) Phase velocity dispersion curves (a) and attenuation dispersion curves (b) of a 4 in. schedule 40 steel hollow cylinder embedded in infinite soil media. Phase velocity dispersion curves (c) and attenuation dispersion curves (d) of a 4 in. schedule 40 steel hollow cylinder coated with 0.27 mm Bitumastic 50 embedded in infinite soil media, showing that 64 elements in the finite soil layer lead to the convergent results in the region of 0.1–0.5 MHz.

Image of FIG. 5.
FIG. 5.

(Color online) Phase velocity dispersion curves (a) and attenuation dispersion curves (b) for a 4 in. schedule 40 steel hollow cylinder embedded in infinite soil media. Phase velocity dispersion curves (c) and attenuation dispersion curves (d) for a 4 in. schedule 40 steel hollow cylinder coated with 0.27 mm Bitumastic 50 embedded in infinite soil media, showing that 5 mm finite soil layer leads to the convergent dispersion curves in the region of 0.1–0.5 MHz.

Image of FIG. 6.
FIG. 6.

(Color online) A plot of wave structures for a 4 in. schedule 40 steel hollow cylinder with 0.27 mm Bitumastic 50 coating embedded in infinite soil media at 0.03 MHz: (a) the L(0,1) mode, (b) the T(0,1) mode, and (c) the L(0,2) mode, showing that displacements vanish in the infinite soil layer for all three wave modes.

Image of FIG. 7.
FIG. 7.

(Color online) A plot of wave structures of a 4 in. schedule 40 steel hollow cylinder with 0.27 mm Bitumastic 50 coating embedded in infinite soil media at 0.5 MHz: (a) the L(0,1) mode, (b) the T(0,1) mode, (c) the L(0,2) mode, (d) the T(0,2) mode, (e) the L(0,3) mode, and (f) the L(0,4) mode, showing that displacements vanish in the infinite soil layer for all six wave modes.

Image of FIG. 8.
FIG. 8.

(Color online) Phase velocity dispersion curves of a 4 in. schedule 40 steel hollow cylinder embedded in infinite soil media, the threshold of the imaginary part of the wave number set as 0.5, circumferential order equal to 0.

Image of FIG. 9.
FIG. 9.

(Color online) Phase velocity dispersion curves (a) and attenuation dispersion curves (b) of a 4 in. schedule 40 steel hollow cylinder embedded in infinite soil media, the threshold of the imaginary part of wave number set as 0.01, circumferential order m = 0, 1, 2, … , 10, showing that flexural modes have higher phase velocities and higher attenuation values.

Image of FIG. 10.
FIG. 10.

(Color online) Phase velocity dispersion curves (a) and attenuation dispersion curves (b) of a 4 in. schedule 40 steel hollow cylinder with 0.27 mm Bitumastic 50 coating embedded in infinite soil media, the threshold of the imaginary part of wave number set as 0.01, circumferential order m = 0, 1, 2, … , 10, showing that non-monotonic features are demonstrated in the region of 0.35–0.4 MHz.

Image of FIG. 11.
FIG. 11.

(Color online) Illustration of the attenuation dispersion curves in Fig. 3 in the range of 0.3–0.45 MHz, A, B, C, and D are four mode points corresponding to the L(0,2) mode, the L(0,3) mode, the L(10,2) mode, and the L(10,3) mode.

Image of FIG. 12.
FIG. 12.

(Color online) Wave structures of four points labeled as (A)–(D) at 0.38 MHz in Fig. 11 : (A) the L(0,2) mode, (B) the L(10,2) mode, (C) the L(10,3) mode, and (D) the L(0,3) mode.

Tables

Generic image for table
TABLE I.

Material properties.

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/content/asa/journal/jasa/129/2/10.1121/1.3531807
2011-02-24
2014-04-25
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Guided wave propagation in single and double layer hollow cylinders embedded in infinite media
http://aip.metastore.ingenta.com/content/asa/journal/jasa/129/2/10.1121/1.3531807
10.1121/1.3531807
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