scholarly journals Dispersion Diagram of Trigonal Piezoelectric Phononic Structures with Langasite Inclusions

Crystals ◽  
2021 ◽  
Vol 11 (5) ◽  
pp. 491
Author(s):  
Edson Miranda ◽  
Clodualdo Aranas ◽  
Samuel Rodrigues ◽  
Hélio Silva ◽  
Gedeon Reis ◽  
...  
Keyword(s):  
Band Gap ◽  
Point Group ◽  
Bulk Wave ◽  
Filling Fraction ◽  
Dispersion Diagram ◽  
Bloch Waves ◽  
Trigonal Structure ◽  
Piezoelectric Coupling ◽  
Transducer Design ◽  
Acoustic Loss

The dispersion relation of elastic Bloch waves in 1-3 piezoelectric phononic structures (PPnSs) with Langasite (La3Ga5SiO14) inclusions in a polymeric matrix is reported. Langasite presents promising material properties, for instance good temperature behaviour, high piezoelectric coupling, low acoustic loss and high quality factor. Furthermore, Langasite belongs to the point group 32 and has a trigonal structure. Thus, the 2-D bulk wave propagation in periodic systems with Langasite inclusions cannot be decoupled into XY and Z modes. The improved plane wave expansion (IPWE) is used to obtain the dispersion diagram of the bulk Bloch waves in 1-3 PPnSs considering the classical elasticity theory and D3 symmetry. Full band gaps are obtained for a broad range of frequency. The piezoelectricity enhances significantly the band gap widths and opens up a narrow band gap in lower frequencies for a filling fraction of 0.5. This study should be useful for surface acoustic wave (SAW) filter and 1-3 piezocomposite transducer design using PPnSs with Langasite.

Full Band-Gap Silicon Phononic Crystals for Surface Acoustic Waves

2006 ◽  
Author(s):  
Saeed Mohammadi ◽  
Abdelkrim Khelif ◽  
Ryan Westafer ◽  
Eric Massey ◽  
William D. Hunt ◽  
...  
Keyword(s):  
Band Gap ◽  
Acoustic Waves ◽  
Phononic Crystal ◽  
Surface Acoustic Waves ◽  
Hexagonal Lattice ◽  
Phononic Crystals ◽  
Bulk Wave ◽  
Filling Fraction ◽  
Phononic Band Gap ◽  
Wide Range

Periodic elastic structures, called phononic crystals, show interesting frequency domain characteristics that can greatly influence the performance of acoustic and ultrasonic devices for several applications. Phononic crystals are acoustic counterparts of the extensively-investigated photonic crystals that are made by varying material properties periodically. Here we demonstrate the existence of phononic band-gaps for surface acoustic waves (SAWs) in a half-space of two dimensional phononic crystals consisting of hexagonal (honeycomb) arrangement of air cylinders in a crystalline Silicon background with low filling fraction. A theoretical calculation of band structure for bulk wave using finite element method is also achieved and shows that there is no complete phononic band gap in the case of the low filling fraction. Fabrication of the holes in Silicon is done by optical lithography and deep Silicon dry etching. In the experimental characterization, we have used slanted finger interdigitated transducers deposited on a thin layer of Zinc oxide (sputtered on top of the phononic crystal structure to excite elastic surface waves in Silicon) to cover a wide range of frequencies. We believe this to be the first reported demonstration of phononic band-gap for SAWs in a hexagonal lattice phononic crystal at such a high frequency.

Flexural Vibration Band Gaps in a Ternary Phononic Crystal Thin Plate

2011 ◽  
Vol 675-677 ◽  
pp. 1085-1088
Author(s):  
Zong Jian Yao ◽  
Gui Lan Yu ◽  
Jian Bao Li
Keyword(s):  
Band Gap ◽  
Thin Plate ◽  
Mass Density ◽  
Phononic Crystal ◽  
Flexural Vibration ◽  
Expansion Method ◽  
Band Gaps ◽  
Physical Parameters ◽  
Vibration Band ◽  
Filling Fraction

The band structures of flexural waves in a ternary locally resonant phononic crystal thin plate are studied using the improved plane wave expansion method. And the thin concrete plate composed of a square array of steel cylinders hemmed around by rubber is considered here. Absolute band gaps of flexural vibration with low frequency are shown. The calculation results show that the band gap width is strongly dependent on the filling fraction, the radius ratio, the mass density and the Young’s modulus contrasts between the core and the coating. So by changing these physical parameters, the required band gap could be obtained.

Transmission properties of locally resonant sonic materials with finite slab thickness

2005 ◽  
Vol 220 (9-10) ◽  
Author(s):  
Kin Hung Fung ◽  
Zhengyou Liu ◽  
Che Ting Chan
Keyword(s):  
Composite Material ◽  
Simple Model ◽  
Band Gap ◽  
Scattering Theory ◽  
Band Gaps ◽  
Slab Thickness ◽  
Frequency Range ◽  
Filling Fraction ◽  
Transmission Properties ◽  
Finite Slab

AbstractUsing multiple-scattering theory, we studied the transmission properties of a slab of composite material that have sonic band gaps due to local resonances. Thin slabs of such material have transmission properties that are apparently different from conventional band gap material. For example, there can be transmission peaks in the frequency range inside the bulk sonic band gap. If the slab thickness is changed, we found that the top of band gap shifts while the bottom of band gap, being pinned by the resonance frequency, does not. By changing the slab thickness, the “effective band gap” may be narrowed or broadened, depending on the filling fraction of the locally resonant units. In order to provide an intuitive understanding of the phenomena, we constructed a simple model to understand the phenomena by comparing its transmission and band structure with that of the locally resonant sonic materials.

Flexural Vibration in a Binary Phononic Crystal Thick Plate with a Point Defect

2010 ◽  
Vol 168-170 ◽  
pp. 1577-1580
Author(s):  
Zong Jian Yao ◽  
Gui Lan Yu ◽  
Yue Sheng Wang ◽  
Jian Bao Li
Keyword(s):  
Frequency Response ◽  
Point Defect ◽  
Band Gap ◽  
Response Function ◽  
Frequency Response Function ◽  
Thick Plate ◽  
Phononic Crystal ◽  
Flexural Vibration ◽  
Rubber Matrix ◽  
Filling Fraction

Based on the finite element method, the propagation of flexural vibration in a binary phononic crystal thick plate with a point defect is studied. The plate is composed of a square array of concrete cylinders embedded in the rubber matrix. Complete band structure and frequency response function of this perfect thick plate indicates the existence of low-frequency absolute band gap. Detailed investigations have been carried out to study the dependence of the width of absolute band gap on both structural and material parameters. For the point defect, the defect modes are localized around the defect, and the frequency and the number of the defect bands are significantly dependent on the filling fraction, the size and the mass density of the defect cylinder. To better support the statement of the defect band structures, we also represent the frequency response function of the propagation of flexural vibration in the thick plate with a point defect. Based on the detailed investigations, both the absolute band gap and the defect bands of a binary thick plate could be modulated with appropriate parameters. It may be useful to vibration control in engineering structure.

Influence of Point Defects on Band Gaps of Fe-Epoxy in Two-Dimensional Phononic Crystal

2013 ◽  
Vol 652-654 ◽  
pp. 1377-1382
Author(s):  
Jiao He ◽  
Guang Hui Fan ◽  
De Xun Zhao ◽  
Ying Kai Liu
Keyword(s):  
Point Defect ◽  
Band Gap ◽  
Nearest Neighbor ◽  
Phononic Crystal ◽  
Expansion Method ◽  
Band Gaps ◽  
Two Dimensional ◽  
Defect States ◽  
Filling Fraction ◽  
Nearest Neighbor Coupling

The band gap of a new two-dimensional phononic crystal was studied by the plane-wave expansion method. The two-dimensional phononic crystal is formed by square-shape array geometry of iron cylinders with square cross section inserted in an epoxy resin. The band gaps of different structures were calculated such as defect-free, single cavity crystal point defect states, crystal point defect states with (10) direction coupling, crystal point defect states with (10) direction next-nearest-neighbor coupling, and crystal point defect states with (11) direction next-nearest-neighbor coupling. Compared with that of defect-free, it is conclude that point defect is beneficial to the production of band gaps. The bandwidth of point defect is about 5 times larger than that of the defect-free crystal with the filling fraction F=0.4. In addition, the maximum number of band gap is in the crystal point defect states with (10) direction next-nearest-neighbor coupling. It will provide a theoretical reference for the manufacture of phononic crystal.

EXISTENCE OF A PHOTONIC BAND GAP AND UNDERLYING PHYSICAL PROCESSES

2001 ◽  
Vol 15 (16) ◽  
pp. 529-534 ◽  
Author(s):  
G. K. JOHRI ◽  
AKHILESH TIWARI ◽  
SAUMYA SAXENA ◽  
MANOJ JOHRI
Keyword(s):  
Refractive Index ◽  
Band Gap ◽  
Lattice Structure ◽  
Photonic Band Gap ◽  
Filling Fraction ◽  
Refractive Index Contrast ◽  
Fcc Lattice ◽  
Index Contrast ◽  
Scattering Strength ◽  
Photonic Band

Mechanisms of the overlapping of gaps due to a refractive index difference minimum and Anderson localization for photonic band gap (PBG) have been used and they give a refractive index contrast difference of less than two percent for X-, L-, and W-points of the Brillouin zone for the pseudogap. Another physical process for the existence of PBG is the use of scattering strength (ε r ≥ 1) for fcc lattice structure. We have found refractive index contrast in the range 2.41–14.21 for the existence of the complete photonic band gap for bound photons (ε r ≥ 1). The lowest limit to yield a gap is 2.41 for valence photons (ε r = 1) at volume filling fraction 85.5% for spherical air atoms and at 14.5% for dielectric spheres. This work is reported for the first time and it is useful for maintaining connectivity and for easier fabrication of photonic crystals.

A Dnv point group structure possessing complete band gap based on gradual heterostructure and self-simulating sphere

2008 ◽  
Vol 93 (20) ◽  
pp. 201902 ◽  
Author(s):  
Tianrui Zhai ◽  
Zhaona Wang ◽  
Rongkuo Zhao ◽  
Jing Zhou ◽  
Dahe Liu ◽  
...  
Keyword(s):  
Band Gap ◽  
Group Structure ◽  
Point Group

Effect of Flexoelectricity on Band Structures of One-Dimensional Phononic Crystals

2013 ◽  
Vol 81 (5) ◽  
Author(s):  
Chenchen Liu ◽  
Shuling Hu ◽  
Shengping Shen
Keyword(s):  
Elastic Wave ◽  
Band Gap ◽  
Periodic Structures ◽  
Scaling Law ◽  
Small Scale ◽  
Filling Fraction ◽  
Size Dependent ◽  
Flexoelectric Effect ◽  
Dependent Theory ◽  
Band Gap Structure

As a size-dependent theory, flexoelectric effect is expected to be prominent at the small scale. In this paper, the band gap structure of elastic wave propagating in a periodically layered nanostructure is calculated by transfer matrix method when the effect of flexoelectricity is taken into account. Detailed calculations are performed for a BaTiO3-SrTiO3 two-layered periodic structure. It is shown that the effect of flexoelectricity can considerably flatten the dispersion curves, reduce the group velocities of the system, and decrease the midfrequency of the band gap. For periodic two-layered structures whose sublayers are of the same thickness, the width of the band gap can be decreased due to flexoelectric effect. It is also unveiled from our analysis that when the filling fraction is small, wider gaps at lower frequencies will be acquired compared with the results without considering flexoelectric effect. In addition, the band gap structures will approach the classical result as the total thickness of the unit cell increases. Our results indicate that the scaling law does not hold when the sizes of the periodic structures reach the nanoscale dimension. Therefore, the consideration of flexoelectric effect on the band structure of a nanosized periodic system is significant for precise manipulation of elastic wave propagation and its practical application.

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