Elastic Wave Localization in Two-Dimensional Phononic Crystals with One-Dimensional Aperiodicity

2011 ◽  
Vol 52-54 ◽  
pp. 1131-1136
Author(s):  
Zhi Zhong Yan ◽  
Chuan Zeng Zhang ◽  
Yue Sheng Wang
Keyword(s):  
Elastic Waves ◽  
Periodic Sequence ◽  
Phononic Crystals ◽  
Two Dimensional ◽  
Wave Localization ◽  
Band Structures ◽  
One Dimensional ◽  
Transmission Coefficients ◽  
Localization Factor ◽  
Match Theory

The band structures of in-plane elastic waves propagating in two-dimensional phononic crystals with one-dimensional aperiodicity are analyzed in this paper. The localization of wave propagation is discussed by introducing the concept of the localization factor that is calculated by the plane-wave-based transfer-matrix method. By treating the aperiodicity as the deviation from the periodicity in a special way, two kinds of aperiodic phononic crystals that have Thue-Morse and Rudin-Shapiro sequence in one direction and translational symmetry in the other direction are considered. The transmission coefficients based on eigenmode match theory are also calculated and the results show the same behaviors as the localization factor does. In the case of Thue-Morse and Rudin-Shapiro structures, the band structures of Thue-Morse sequence exhibit similarities with quasi-periodic sequence not present in the results of Rudin-Shapiro sequence.

Elastic Wave Localization in Layered Phononic Crystals With Fractal Superlattices

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
Zhi-zhong Yan ◽  
Chuanzeng Zhang ◽  
Yue-sheng Wang
Keyword(s):  
Wave Propagation ◽  
Elastic Waves ◽  
Golden Section ◽  
Structure Design ◽  
Phononic Crystals ◽  
Wave Localization ◽  
Fractal Structures ◽  
Localization Factor ◽  
Time Harmonic ◽  
Approximate Similarity

In this paper, localization phenomena of in-plane time-harmonic elastic waves propagating in layered phononic crystals (PNCs) with different fractal superlattices are studied. For this purpose, oblique wave propagation in layered structures is considered. To describe wave localization phenomena, the localization factor is applied and computed by the transfer matrix method. Three typical fractal superlattices are considered, namely, the Cantorlike fractal superlattice (CLFSL), the golden-section fractal superlattice (GSFSL), and the Fibonacci fractal superlattice (FFSL). Numerical results for the localization factors of CLFSL, GSFSL, and FFSL are presented and analyzed. The results show that the localization factor of a CLFSL exhibits an approximate similarity and band-splitting properties. The number of decomposed bandgaps of the GSFSL and FFSL follows the composition of the special fractal structures. In addition, with increasing fractal series, the value of the localization factor is enlarged. These results are of great importance for structure design of fractal PNCs.

SYMMETRY AND COUPLING EFFICIENCY OF THE DEFECT MODES IN TWO-DIMENSIONAL PHONONIC CRYSTALS

2007 ◽  
Vol 21 (22) ◽  
pp. 1479-1488 ◽  
Author(s):  
Y. J. CAO ◽  
Y. Z. LI
Keyword(s):  
Phononic Crystal ◽  
Plane Waves ◽  
Coupling Efficiency ◽  
Phononic Crystals ◽  
Two Dimensional ◽  
Defect Modes ◽  
Transmission Coefficients ◽  
Resonant Modes ◽  
Incident Plane ◽  
Match Theory

We study theoretically the symmetric property and coupling efficiency of the defect modes in a two-dimensional phononic crystal by calculating band structures, field distributions and transmission coefficients of the defect modes. The results show that the point defect could act as a microcavity surrounded by the phononic crystal, and the confining ability of the phononic crystal to the resonant modes strongly depends on the thickness of the phononic crystal. By investigating the transmission spectra, we also find that the defect modes cannot be absolutely excited by the normally incident plane waves. The transmission coefficients are calculated by using the eigen-mode match theory method under the supercell technique, which is applied to the phononic crystals with the defects for the first time.

Influence of Random Disorders on Anti-Plane Waveguiding Modes in a Two-Dimensional Phononic Crystal

2011 ◽  
Vol 197-198 ◽  
pp. 352-357
Author(s):  
A Li Chen ◽  
Yue Sheng Wang ◽  
Chuan Zeng Zhang
Keyword(s):  
Phononic Crystal ◽  
Expansion Method ◽  
Guided Wave ◽  
Phononic Crystals ◽  
Two Dimensional ◽  
Wave Localization ◽  
Plane Wave Expansion Method ◽  
Band Structures ◽  
Line Defects ◽  
Random Disorder

In this paper, combined with the supercell technique, the plane wave expansion method is used to calculate the band structures of the two-dimensional phononic crystals with line defects and the random disorders in either radius or location of the scatterers. Phononic systems with plumbum scatterers embedded in an epoxy matrix are calculated in detail. The influences of the random disorder on the band structures of anti-plane waveguiding modes will be discussed. The displacement distributions are calculated to show the wave localization phenomenon. Propagation of the guided wave in the phononic crystals with different disordered degree is studied. The analysis is relevant to the assessment of the influences of manufacture errors on wave behaviors in waveguiding phononic crystals as well as the possible control of wave propagation by intentionally introducing disorders into the systems.

Low frequency phononic band structures in two-dimensional arc-shaped phononic crystals

2012 ◽  
Vol 376 (33) ◽  
pp. 2256-2263 ◽  
Author(s):  
Zhenlong Xu ◽  
Fugen Wu ◽  
Zhongning Guo
Keyword(s):  
Low Frequency ◽  
Phononic Crystals ◽  
Two Dimensional ◽  
Band Structures

Tunable Band Gaps of Acoustic Waves in Two-Dimensional Phononic Crystals With Reticular Band Structures

2009 ◽  
Author(s):  
Zi-Gui Huang ◽  
Yunn-Lin Hwang ◽  
Pei-Yu Wang ◽  
Yen-Chieh Mao
Keyword(s):  
Acoustic Waves ◽  
Composite Structures ◽  
Phononic Crystals ◽  
Band Gaps ◽  
Sound Insulation ◽  
Two Dimensional ◽  
The Finite Element Method ◽  
Elastic Band ◽  
Band Structures ◽  
Elastic Band Gaps

The excellent applications and researches of so-called photonic crystals raise the exciting researches of phononic crystals. By the analogy between photon and phonon, repetitive composite structures that are made up of different elastic materials can also prevent elastic waves of some certain frequencies from passing by, i.e., the frequency band gap features also exist in acoustic waves. In this paper, we present the results of the tunable band gaps of acoustic waves in two-dimensional phononic crystals with reticular band structures using the finite element method. Band gaps variations of the bulk modes due to different thickness and angles of reticular band structures are calculated and discussed. The results show that the total elastic band gaps for mixed polarization modes can be enlarged or reduced by adjusting the orientation of the reticular band structures. The phenomena of band gaps of elastic or acoustic waves can potentially be utilized for vibration-free, high-precision mechanical systems, and sound insulation.

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