Flexural Vibration in a Ternary Locally Resonant Phononic Crystal Thin Plate with Defects

2010 ◽  
Vol 150-151 ◽  
pp. 1282-1285
Author(s):  
Zong Jian Yao ◽  
Gui Lan Yu ◽  
Yue Sheng Wang ◽  
Jian Bao Li
Keyword(s):  
Point Defect ◽  
Thin Plate ◽  
Mass Density ◽  
Phononic Crystal ◽  
Flexural Vibration ◽  
Defect Mode ◽  
Expansion Method ◽  
Flexural Waves ◽  
Filling Fraction ◽  
Linear Defects

The improved supercell plane wave expansion method is applied to theoretically study the propagation of flexural waves in a ternary locally resonant phononic crystal thin plate with a point defect and linear defects. The thin concrete plate composed of a square array of steel cylinders hemmed around by rubber is considered here. Absolute band gaps in low frequency are obtained. For the point defect, the defect mode is localized around the defect, and the magnitude of the resonant defect mode is strongly dependent on the defect filling fraction, mass density and Young’s modulus of the defect cylinder. For the straight linear defects, several resonant linear defect bands appear inside the absolute band gap. And the displacement distributions show that the flexural waves could well propagate along the linear defects.

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.

Finite Element Method for Analysis of Flexural Vibration Propagating in Ternary Phononic Crystal Thin Plates

2012 ◽  
Vol 256-259 ◽  
pp. 596-599
Author(s):  
Zong Jian Yao ◽  
Gui Lan Yu ◽  
Yue Sheng Wang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Point Defect ◽  
Phononic Crystal ◽  
Flexural Vibration ◽  
Expansion Method ◽  
Square Lattice ◽  
Thin Plates ◽  
Response Curves ◽  
Element Method

Propagation of flexural vibration in a ternary phononic crystal thin plate with a point defect are explored using finite element method. The thin concrete plate is composed of steel cylinders hemmed around by rubber with a square lattice. Absolute band gaps, point defect bands and transmission response curves with low frequency are investigated. Comparing the results of finite element method with that of improved plane wave expansion method, precise identifications are obtained to identify the point defect states. The results show that the finite element method is suitable for the exploring of flexural vibration propagating in ternary phononic crystal thin plates.

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.

scholarly journals Highly Localized and Efficient Energy Harvesting in a Phononic Crystal Beam: Defect Placement and Experimental Validation

Crystals ◽  
2019 ◽  
Vol 9 (8) ◽  
pp. 391 ◽  
Author(s):  
Xu-Feng Lv ◽  
Xiang Fang ◽  
Zhi-Qiang Zhang ◽  
Zhi-Long Huang ◽  
Kuo-Chih Chuang
Keyword(s):  
Energy Harvesting ◽  
Point Defect ◽  
Polyvinylidene Fluoride ◽  
Experimental Validation ◽  
Flexural Rigidity ◽  
Phononic Crystal ◽  
Defect Mode ◽  
Unit Cell ◽  
Pvdf Film ◽  
Efficient Energy

We study energy harvesting in a binary phononic crystal (PC) beam at the defect mode. Specifically, we consider the placement of a mismatched unit cell related to the excitation point. The mismatched unit cell contains a perfect segment and a geometrically mismatched one with a lower flexural rigidity which serves as a point defect. We show that the strain in the defect PC beam is much larger than those in homogeneous beams with a defect segment. We suggest that the defect segment should be arranged in the first unit cell, but not directly connected to the excitation source, to achieve efficient less-attenuated localized energy harvesting. To harvest the energy, a polyvinylidene fluoride (PVDF) film is attached on top of the mismatched segment. Our numerical and experimental results indicate that the placement of the mismatched segment, which has not been addressed for PC beams under mechanical excitation, plays an important role in efficient energy harvesting based on the defect mode.

Effects of rotated square inserts on the longitudinal vibration band gaps in thin phononic crystal plates

2015 ◽  
Vol 29 (20) ◽  
pp. 1550105
Author(s):  
Haojiang Zhao ◽  
Rongqiang Liu ◽  
Chuang Shi ◽  
Hongwei Guo ◽  
Zongquan Deng
Keyword(s):  
Plane Wave ◽  
Longitudinal Vibration ◽  
Phononic Crystal ◽  
Expansion Method ◽  
Band Gaps ◽  
Vibration Band ◽  
Plane Wave Expansion ◽  
Plane Wave Expansion Method ◽  
Filling Fraction ◽  
Gap Width

Longitudinal vibration of thin phononic crystal plates with a hybrid square-like array of square inserts is investigated. The plane wave expansion method is used to calculate the vibration band structure of the plate. Numerical results show that rotated square inserts can open several vibration gaps, and the band structures are twisted because of the rotation of inserts. Filling fraction and material of the insert affect the change law of the gap width versus the rotation angles of square inserts.

Propagation of flexural waves in phononic crystal thin plates with linear defects

2010 ◽  
Vol 11 (10) ◽  
pp. 827-834 ◽  
Author(s):  
Zong-jian Yao ◽  
Gui-lan Yu ◽  
Yue-sheng Wang ◽  
Zhi-fei Shi ◽  
Jian-bao Li
Keyword(s):  
Phononic Crystal ◽  
Thin Plates ◽  
Flexural Waves ◽  
Linear Defects

The point defect and eigenfield distribution for two-dimensional function photonic crystal

2018 ◽  
Vol 32 (25) ◽  
pp. 1830008 ◽  
Author(s):  
Ji-Ping Liu ◽  
Hai-Bo Li ◽  
Xiang-Dong Meng ◽  
Xiao-Ru Zhang ◽  
Han Liu ◽  
...  
Keyword(s):  
Dielectric Constant ◽  
Photonic Crystal ◽  
Point Defect ◽  
Kerr Effect ◽  
Defect Mode ◽  
Expansion Method ◽  
Two Dimensional ◽  
Plane Wave Expansion Method ◽  
Electro Optic ◽  
Space Coordinate

With the plane wave expansion method, we introduced the concept and theory of two-dimensional function photonic crystal, and compared the theoretical difference of two-dimensional function photonic crystal with the conventional photonic crystal. In Numerical calculation, with COMSOL software based on finite element method, we have studied the bandgap structure, defect mode and eigenfield distribution for the two-dimensional function photonic crystal with and without point defect. For the two-dimensional function photonic crystal, the dielectric constant of dielectric column is the space coordinate function, which can be realized by the electro-optic effect and the Kerr effect. In the paper, we studied the dielectric constant function form is [Formula: see text](r) = kr + b, and the parameters k and b can be adjusted by changing the electric field or light intensity applied to the dielectric column. By changing the parameters k or b of the dielectric column dielectric constant, we found the two-dimensional function photonic crystal transmission characteristics have the adjustability, i.e., the bandgap structure, the bandgap position and width, the defect mode position, width and number and the defect mode eigenfield distribution can be changed by adjusting the parameters k or b, which can be used to conveniently design the bandgap structure that we need. These conclusions will provide important theoretical basis and methods for optical devices design.

Linear Defect States of Phononic Crystal Thin Plates – An Application of Finite Element Method

2013 ◽  
Vol 652-654 ◽  
pp. 48-51
Author(s):  
Zong Jian Yao ◽  
Gui Lan Yu ◽  
Yue Sheng Wang ◽  
Wen Jun Hu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Phononic Crystal ◽  
Flexural Vibration ◽  
Expansion Method ◽  
Square Lattice ◽  
Thin Plates ◽  
Defect States ◽  
Response Curves ◽  
Element Method

In this paper, propagation of flexural vibration in phononic crystal thin plates with straight, bending or branching linear defects are explored using finite element method. The plate is composed of an array of circular crystalline Al2O3 cylinders embedded periodically in the epoxy matrix with a square lattice. The numerical results showed that accurate band structures and transmission response curves could be obtained by finite element method compared with that of improved plane wave expansion method. The exploration indicated that finite element method is efficient and suitable in dealing with the wave propagation in phononic crystal, and displays potential abilities in dealing with complex structures.

scholarly journals Plane Wave-Perturbative Method for Evaluating the Effective Speed of Sound in 1D Phononic Crystals

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
J. Flores Méndez ◽  
M. Salazar Villanueva ◽  
R. C. Ambrosio Lázaro ◽  
B. Calixto Sirene ◽  
M. L. Mota González ◽  
...  
Keyword(s):  
Elastic Moduli ◽  
Mass Density ◽  
Wave Length ◽  
Phononic Crystal ◽  
Plane Waves ◽  
Phononic Crystals ◽  
Effective Parameters ◽  
Filling Fraction ◽  
Perturbative Method ◽  
Sound Velocities

A method for calculating the effective sound velocities for a 1D phononic crystal is presented; it is valid when the lattice constant is much smaller than the acoustic wave length; therefore, the periodic medium could be regarded as a homogeneous one. The method is based on the expansion of the displacements field into plane waves, satisfying the Bloch theorem. The expansion allows us to obtain a wave equation for the amplitude of the macroscopic displacements field. From the form of this equation we identify the effective parameters, namely, the effective sound velocities for the transverse and longitudinal macroscopic displacements in the homogenized 1D phononic crystal. As a result, the explicit expressions for the effective sound velocities in terms of the parameters of isotropic inclusions in the unit cell are obtained: mass density and elastic moduli. These expressions are used for studying the dependence of the effective, transverse and longitudinal, sound velocities for a binary 1D phononic crystal upon the inclusion filling fraction. A particular case is presented for 1D phononic crystals composed of W-Al and Polyethylene-Si, extending for a case solid-fluid.

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