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.

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.

Thermal Tuning of Vibration Band Gaps in Thin Phononic Crystal Plates with Nitinol

2014 ◽  
Vol 597 ◽  
pp. 78-83 ◽  
Author(s):  
Hao Jiang Zhao ◽  
Rong Qiang Liu ◽  
Hong Wei Guo
Keyword(s):  
Plane Wave ◽  
Phononic Crystal ◽  
Band Gaps ◽  
Vibration Band ◽  
Plane Wave Expansion ◽  
Band Structures ◽  
Filling Fraction ◽  
Wave Expansion ◽  
Square Array ◽  
Thermal Tuning

Vibration band structures of thin phononic crystal plates (PCPs) with square array and graphite array of nitinol inserts are calculated by the plane wave expansion (PWE) method. The influences of filling fraction are considered when investigating the effects of the varying temperature on the band gaps. Vibration band gaps of these PCPs can be tuned by changing temperature. This study will be useful in designing PCPs with tunable gaps.

The band gap properties of the three-component semi-infinite plate-like LRPC by using PWE/FE method

2018 ◽  
Vol 32 (16) ◽  
pp. 1850173
Author(s):  
Denghui Qian ◽  
Jianchun Wang
Keyword(s):  
Finite Element ◽  
Band Structure ◽  
Band Gap ◽  
Phononic Crystal ◽  
Infinite Plate ◽  
Frequency Range ◽  
Fe Method ◽  
Mass Model ◽  
Rubber Layer ◽  
The Matrix

This paper applies coupled plane wave expansion and finite element (PWE/FE) method to calculate the band structure of the proposed three-component semi-infinite plate-like locally resonant phononic crystal (LRPC). In order to verify the accuracy of the result, the band structure calculated by PWE/FE method is compared to that calculated by the traditional finite element (FE) method, and the frequency range of the band gap in the band structure is compared to that of the attenuation in the transmission power spectrum. Numerical results and further analysis demonstrate that a band gap is opened by the coupling between the dominant vibrations of the rubber layer and the matrix modes. In addition, the influences of the geometry parameters on the band gap are studied and understood with the help of the simple “base-spring-mass” model, the influence of the viscidity of rubber layer on the band gap is also investigated.

scholarly journals Modelling Propagating Bloch Waves in Magnetoelectroelastic Phononic Structures with Kagomé Lattice Using the Improved Plane Wave Expansion

Crystals ◽  
2020 ◽  
Vol 10 (7) ◽  
pp. 586 ◽  
Author(s):  
Edson Jansen Pedrosa de Miranda ◽  
Samuel Filgueiras Rodrigues ◽  
Clodualdo Aranas ◽  
Hélio Vitor Cantanhêde da Silva ◽  
Eden Santos Silva ◽  
...  
Keyword(s):  
Plane Wave ◽  
Transverse Isotropy ◽  
Phononic Crystal ◽  
Plane Wave Expansion ◽  
Kagome Lattice ◽  
Dispersion Diagram ◽  
Kagomé Lattice ◽  
Wave Expansion ◽  
Piezomagnetic Effects ◽  
Classical Elasticity Theory

We studied the dispersion diagram of a 2D magnetoelectroelastic phononic crystal (MPnC) with Kagomé lattice. The MPnC is composed of BaTiO3–CoFe2O4 circular scatterers embedded in a polymeric matrix. The improved plane wave expansion (IPWE) approach was used to calculate the dispersion diagram (only propagating modes) of the MPnC considering the classical elasticity theory, solid with transverse isotropy and wave propagation in the xy plane. Complete Bragg-type forbidden bands were observed for XY and Z modes. The piezoelectric and the piezomagnetic effects significantly influenced the forbidden band widths and localizations. This investigation can be valuable for elastic wave manipulation using smart phononic crystals with piezoelectric and piezomagnetic effects.

Absolute Band Gaps in Two-Dimensional Phononic Crystal Plates

2006 ◽  
Author(s):  
Je´roˆme Vasseur ◽  
Pierre A. Deymier ◽  
Bahram Djafari-Rouhani ◽  
Yan Pennec
Keyword(s):  
Band Structure ◽  
Phononic Crystal ◽  
Plate Thickness ◽  
Two Dimensional ◽  
Plane Wave Expansion ◽  
Elastic Band ◽  
Band Structures ◽  
Super Cell ◽  
Order Of Magnitude ◽  
Crystal Dispersion

The elastic band structures of two-dimensional phononic crystal plates are computed with the help of a super-cell plane wave expansion (PWE) method. These band structures strongly differ from the infinite 2D phononic crystal dispersion curves. In particular, these band structures exhibit surface modes and guided modes. The influence of the constituent materials, of the plate thickness and of the geometry of the array on the band structure is investigated. We focus more specifically on determining the thicknesses of the plate for which absolute forbidden bands exist. Namely, we show that absolute forbidden bands occur in the band structure if the thickness of the plate is of the same order of magnitude as the periodicity of the array of inclusions.

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