scholarly journals An Enhanced Plane Wave Expansion Method to Solve Piezoelectric Phononic Crystal with Resonant Shunting Circuits

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Ziyang Lian ◽  
Shan Jiang ◽  
Hongping Hu ◽  
Longxiang Dai ◽  
Xuedong Chen ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Plane Wave ◽  
Phononic Crystal ◽  
Expansion Method ◽  
Band Gaps ◽  
Plane Wave Expansion ◽  
One Dimensional ◽  
Wave Expansion ◽  
Element Method

An enhanced plane wave expansion (PWE) method is proposed to solve piezoelectric phononic crystal (PPC) connected with resonant shunting circuits (PPC-C), which is named as PWE-PPC-C. The resonant shunting circuits can not only bring about the locally resonant (LR) band gap for the PPC-C but also conveniently tune frequency and bandwidth of band gaps through adjusting circuit parameters. However, thus far, more than one-dimensional PPC-C has been studied just by Finite Element method. Compared with other methods, the PWE has great advantages in solving more than one-dimensional PC as well as various lattice types. Nevertheless, the conventional PWE cannot accurately solve coupling between the structure and resonant shunting circuits of the PPC-C since only taking one-way coupling from displacements to electrical parameters into consideration. A two-dimensional PPC-C model of orthorhombic lattice is established to demonstrate the whole solving process of PWE-PPC-C. The PWE-PPC-C method is validated by Transfer Matrix method as well as Finite Element method. The dependence of band gaps on circuit parameters has been investigated in detail by PWE-PPC-C. Its advantage in solving various lattice types is further illustrated by calculating the PPC-C of triangular and hexagonal lattices, respectively.

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.

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.

scholarly journals Using PWE/FE Method to Calculate the Band Structures of the Semi-Infinite PCs: Periodic in x–y Plane and Finite in z -direction

2017 ◽  
Vol 42 (4) ◽  
pp. 735-742 ◽  
Author(s):  
Denghui Qian ◽  
Zhiyu Shi
Keyword(s):  
Finite Element ◽  
Band Structure ◽  
Plane Wave ◽  
Composite Structures ◽  
Phononic Crystal ◽  
Plane Wave Expansion ◽  
Fe Method ◽  
Band Structures ◽  
Wave Expansion ◽  
Elastic Composite

Abstract This paper introduces the concept of semi-infinite phononic crystal (PC) on account of the infinite periodicity in x-y plane and finiteness in z-direction. The plane wave expansion and finite element methods are coupled and formulized to calculate the band structures of the proposed periodic elastic composite structures based on the typical geometric properties. First, the coupled plane wave expansion and finite element (PWE/FE) method is applied to calculate the band structures of the Pb/rubber, steel/epoxy and steel/aluminum semi-infinite PCs with cylindrical scatters. Then, it is used to calculate the band structure of the Pb/rubber semi-infinite PC with cubic scatter. Last, the band structure of the rubbercoated Pb/epoxy three-component semi-infinite PC is calculated by the proposed method. Besides, all the results are compared with those calculated by the finite element (FE) method implemented by adopting COMSOL Multiphysics. Numerical results and further analysis demonstrate that the proposed PWE/FE method has strong applicability and high accuracy.

Study on the Vibration Reduction of Phononic Crystal Structural Plate

2014 ◽  
Vol 543-547 ◽  
pp. 3900-3903
Author(s):  
Yu Yang He ◽  
Xiao Xiong Jin
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Propagation ◽  
Plane Wave ◽  
Elastic Wave ◽  
Band Gap ◽  
Phononic Crystal ◽  
Vibration Reduction ◽  
Plane Wave Expansion ◽  
Crystal Structural

Plane wave expansion (PWE) method and finite element method (FEM) are applied to analyze the vibration reduction characteristic of the phononic crystal structural plate, and the results of two methods are consistent. The range of band gap is acquired, which certain frequent elastic wave propagation is forbidden.

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.

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