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Large bandgaps of two-dimensional phononic crystals with cross-like holes
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10.1063/1.3665205
/content/aip/journal/jap/110/11/10.1063/1.3665205
http://aip.metastore.ingenta.com/content/aip/journal/jap/110/11/10.1063/1.3665205

Figures

Image of FIG. 1.
FIG. 1.

Cross-sections and finite element models of the unit cells of the 2D PNCs with (a) “+”- and (b) “x”-holes.

Image of FIG. 2.
FIG. 2.

(Color online) Band structures of the PNC systems with (a) square, (b) “+”-, (c) “x”-, and (d) circular holes. The red solid and black dashed lines represent the mixed and shear wave modes, respectively.

Image of FIG. 3.
FIG. 3.

(Color online) Vibration modes at the edge of the lowest bandgap for PNCs with “+”-holes. Panels (a)–(d) correspond to points M1, M2, S1, and S2 in Fig. 2(b), respectively.

Image of FIG. 4.
FIG. 4.

(Color online) Vibration modes at the edge of the lowest bandgap for PNCs with “x”-holes. Panels (a)–(d) correspond to points M3, M4, S3, and S4 in Fig. 2(c), respectively.

Image of FIG. 5.
FIG. 5.

(Color online) Vibration modes at the edge of the lowest bandgap for PNCs with circular holes. Panels (a)–(d) correspond to points M5, M6, S5, and S6 in Fig. 2(d), respectively.

Image of FIG. 6.
FIG. 6.

Variation of the normalized width of the lowest bandgap for the (a) mixed and the (b) shear wave modes with the geometry parameters b/a and c/a. The regions below and above the dashed line correspond to the results for the systems with “+”- and “x”-holes, respectively.

Image of FIG. 7.
FIG. 7.

(Color online) Variation of the upper and lower edges of the bandgaps in the system of “+”-holes with the geometry parameter (a) b/a (c/a = 0.25) or (b) c/a (b/a = 0.9). The solid and dashed lines represent the upper and lower edges of the bandgaps, respectively. The open and solid symbols represent the shear and mixed modes, respectively. The dash-dotted lines show the results for the reduced frequencies of the lower edge modes predicted by the equivalent spring-mass model.

Image of FIG. 8.
FIG. 8.

Variation of the normalized width of the lowest bandgap for the (a) mixed and (b) shear wave modes in systems of “x”-holes with the geometry parameters b/a and d/a (c/a = 0.9).

Image of FIG. 9.
FIG. 9.

(Color online) Variation of the upper and lower edges of the bandgaps in the system of “x”-holes (d = 0.98b) with the geometry parameter (a) c/a (b/a = 0.35) or (b) b/a (c/a = 0.9). The solid and dashed lines represent the upper and lower edges of the bandgaps, respectively. The open and solid symbols represent the shear and mixed modes, respectively. The dash-dotted line show the results for the reduced frequencies of the lower edge modes predicted by the equivalent spring-mass model. The dotted line shows the modified results from the Euler-beam model.

Image of FIG. 10.
FIG. 10.

(Color online) Band structures of the PNC systems with (a) square, (b) “x”-, and (c) “+”-holes rotated by 45°. The red solid and black dashed lines represent the mixed and shear wave modes, respectively.

Image of FIG. 11.
FIG. 11.

(Color online) Vibration modes at the edge of the lowest bandgap for PNCs with square holes rotated by 45°. Panels (a)–(d) correspond to points M7, M8, S7, and S8 in Fig. 10(a), respectively.

Image of FIG. 12.
FIG. 12.

(Color online) Vibration modes at the edge of the lowest bandgap for PNCs with “x”-holes rotated by 45°. Panels (a)–(d) correspond to points M9, M10, S9, and S10 in Fig. 10(b), respectively.

Image of FIG. 13.
FIG. 13.

(Color online) Variation of the upper and lower edges of the bandgaps in the systems of (a) square, (b) “x”-, and (c) “+”-holes with the rotation angle. The solid and dashed lines represent the upper and lower edges of the bandgaps, respectively. The open and solid symbols represent the shear and mixed modes, respectively.

Tables

Generic image for table
Table I.

Calculation of the effective mass and stiffness of the proposed spring-mass model for the lower edge modes of the lowest bandgap.

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/content/aip/journal/jap/110/11/10.1063/1.3665205
2011-12-09
2014-04-24
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Large bandgaps of two-dimensional phononic crystals with cross-like holes
http://aip.metastore.ingenta.com/content/aip/journal/jap/110/11/10.1063/1.3665205
10.1063/1.3665205
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