Acoustic band gaps with diffraction gratings in a two-dimensional phononic crystal with a square lattice in water

2016 ◽  
Vol 68 (8) ◽  
pp. 989-993 ◽  
Author(s):  
Kang Il Lee ◽  
Hwi Suk Kang ◽  
Suk Wang Yoon
Keyword(s):  
Phononic Crystal ◽  
Diffraction Gratings ◽  
Band Gaps ◽  
Square Lattice ◽  
Two Dimensional

Locally resonant surface acoustic wave band gaps in a two-dimensional phononic crystal of pillars on a surface

2010 ◽  
Vol 81 (21) ◽  
Author(s):  
Abdelkrim Khelif ◽  
Younes Achaoui ◽  
Sarah Benchabane ◽  
Vincent Laude ◽  
Boujamaa Aoubiza
Keyword(s):  
Acoustic Wave ◽  
Surface Acoustic Wave ◽  
Phononic Crystal ◽  
Band Gaps ◽  
Wave Band ◽  
Two Dimensional

Surface Effects on Bandgaps of Transverse Waves Propagating in Two Dimensional Phononic Crystals with Nanosized Holes

2011 ◽  
Vol 675-677 ◽  
pp. 611-614 ◽  
Author(s):  
Ni Zhen ◽  
Yue Sheng Wang
Keyword(s):  
Laplace Equation ◽  
Surface Effect ◽  
Phononic Crystal ◽  
Surface Effects ◽  
Phononic Crystals ◽  
Square Lattice ◽  
Two Dimensional ◽  
Transverse Waves ◽  
Circular Holes

In this paper, a method based on the displacement-traction map is developed to calculate the bandgaps of transverse waves propagating in a 2D phononic crystal composed of nanosized circular holes in a square lattice. The Young-Laplace equation is employed to take into account of the surface effects of the nanosized holes. Detailed calculations are performed for the system with nanosized circular holes in an aluminum host with or without the surface effect. The result shows that all bands descend with the first bandgap becoming wider due to the existence of the surface effects.

Existence of complete band gaps in 2D steel-water phononic crystal with square lattice

2010 ◽  
Vol 5 (4) ◽  
pp. 450-454 ◽  
Author(s):  
Cunfu He ◽  
Huanyu Zhao ◽  
Ruiju Wei ◽  
Bin Wu
Keyword(s):  
Phononic Crystal ◽  
Band Gaps ◽  
Square Lattice

Phononic Band Gaps in Al2O3/Epoxy Composite

2018 ◽  
Vol 912 ◽  
pp. 112-117 ◽  
Author(s):  
Edson Jansen Pedrosa Miranda Jr. ◽  
J.M.C. dos Santos
Keyword(s):  
Cross Section ◽  
Transverse Vibration ◽  
Elastic Waves ◽  
Epoxy Composite ◽  
Phononic Crystal ◽  
Band Gaps ◽  
Square Lattice ◽  
Plane Wave Expansion ◽  
Phononic Band Gaps ◽  
Angle Of Rotation

In this study, we have investigated the band structure of elastic waves propagating in a phononic crystal, consisting of an epoxy matrix reinforced by Al2O3 inclusions in a square and hexagonal lattices. We also studied the influence of the inclusion geometry cross section – circular, hollow circular, square and rotated square with a 45° angle of rotation with respect to the x, y axes. The plane wave expansion (PWE) method is used to solve the wave equation considering the wave propagation in the xy plane (longitudinal-transverse vibration, XY mode, and transverse vibration, Z mode). The complete band gaps between the XY and Z modes are observed to circular, square and rotated square cross section inclusion and the best performance is for rotated square cross section inclusion in a square lattice. We suggest that the Al2O3/epoxy composite is feasible for vibrations management.

Absolute photonic band gaps of two-dimensional square-lattice photonic crystals with Taiji-shaped dielectric rods

2011 ◽  
Vol 284 (14) ◽  
pp. 3491-3496 ◽  
Author(s):  
Xing-Dao He ◽  
Shou-Xiao Du ◽  
Bin Liu ◽  
Shu-Jing Li ◽  
Shan Li
Keyword(s):  
Photonic Crystals ◽  
Band Gaps ◽  
Square Lattice ◽  
Two Dimensional ◽  
Photonic Band Gaps ◽  
Photonic Band

Electrons in a square lattice

2021 ◽  
pp. 352-362
Author(s):  
Geoffrey Brooker
Keyword(s):  
Periodic Potential ◽  
Band Gaps ◽  
Three Dimensions ◽  
Square Lattice ◽  
One Dimension ◽  
Two Dimensional ◽  
Effective Masses ◽  
Overlapping Bands

“Electrons in a square lattice” describes how a two-dimensional square lattice gives a helpful case intermediate between one dimension and the complication of three dimensions. The “empty lattice” divides up k-space into Brillouin zones in anticipation of a periodic potential whose period is given but whose magnitude is at this stage zero. A wooden model uses height to represent energy. Rearranging the model's pieces into the reduced-zone scheme displays how electrons can have surprising energy–wavevector relations, including overlapping bands, anisotropic effective masses, and indirect band gaps.

Band Gaps of Two-Dimensional Square-Lattice Photonic Crystal with Button-Shaped Dielectric Rods

2011 ◽  
Vol 216 ◽  
pp. 285-289
Author(s):  
S.X. Du ◽  
X. D. He ◽  
B. Liu ◽  
S. J. Li ◽  
Z.M. Zhang ◽  
...  
Keyword(s):  
Photonic Crystal ◽  
Plane Wave ◽  
Band Gap ◽  
Expansion Method ◽  
Band Gaps ◽  
Square Lattice ◽  
Two Dimensional ◽  
Plane Wave Expansion ◽  
Plane Wave Expansion Method ◽  
Wave Expansion

In this paper, a new structure of two-dimensional (2D) square-lattice photonic crystal (SLPC) with button-shaped dielectric rods (BSDRs) is designed, and the properties of band gaps are analyzed by Plane Wave Expansion Method (PWM). The optimal samples that possess the width of absolute band gap are obtained by scanning the three parameters: the radius of large circular R in button mark, the ratio of the radius of small circular to the radius of large circular r/R, and the rotating angle of button mark Ө. It is shown that when r/R=0.485, R=0.406um, and Ө =750, the largest absolute band gap of 0.0406 (ωa/2πc) exists for normalized frequencies in the range 0.7501 to 0.7910 (ωa/2πc). Besides，we can get at most five absolute band gaps when r/R=0.485, R=0.406um, and Ө =600.

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