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 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.

Modeling and Analysis of Nonlinear Wave Propagation in One-Dimensional Phononic Structures

2018 ◽  
Vol 140 (6) ◽  
Author(s):  
M. Liu ◽  
W. D. Zhu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Propagation ◽  
Band Structure ◽  
Band Gap ◽  
Nonlinear Wave ◽  
Elastic Waves ◽  
Propagation Characteristics ◽  
Nonlinear Wave Propagation ◽  
Weakly Nonlinear

Different from elastic waves in linear periodic structures, those in phononic crystals (PCs) with nonlinear properties can exhibit more interesting phenomena. Linear dispersion relations cannot accurately predict band-gap variations under finite-amplitude wave motions; creating nonlinear PCs remains challenging and few examples have been studied. Recent studies in the literature mainly focus on discrete chain-like systems; most studies only consider weakly nonlinear regimes and cannot accurately obtain some relations between wave propagation characteristics and general nonlinearities. This paper presents propagation characteristics of longitudinal elastic waves in a thin rod and coupled longitudinal and transverse waves in an Euler–Bernoulli beam using their exact Green–Lagrange strain relations. We derive band structure relations for a periodic rod and beam and predict their nonlinear wave propagation characteristics using the B-spline wavelet on the interval (BSWI) finite element method. Influences of nonlinearities on wave propagation characteristics are discussed. Numerical examples show that the proposed method is more effective for nonlinear static and band structure problems than the traditional finite element method and illustrate that nonlinearities can cause band-gap width and location changes, which is similar to results reported in the literature for discrete systems. The proposed methodology is not restricted to weakly nonlinear systems and can be used to accurately predict wave propagation characteristics of nonlinear structures. This study can provide good support for engineering applications, such as sound and vibration control using tunable band gaps of nonlinear PCs.

scholarly journals Study on Low-Frequency Band Gap Characteristics of a New Helmholtz Type Phononic Crystal

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1379
Author(s):  
Dong-Hai Han ◽  
Jing-Bo Zhao ◽  
Guang-Jun Zhang ◽  
Hong Yao
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Band Gap ◽  
Lattice Constant ◽  
Phononic Crystal ◽  
Low Frequency ◽  
Equivalent Model ◽  
Frequency Noise ◽  
The Finite Element Method ◽  
Symmetric Structure

In order to solve the problem of low-frequency noise of aircraft cabins, this paper presents a new Helmholtz type phononic crystal with a two-dimensional symmetric structure. Under the condition of the lattice constant of 62 mm, the lower limit of the first band gap is about 12 Hz, and the width is more than 10 Hz, thus the symmetric structure has distinct sound insulation ability in the low-frequency range. Firstly, the cause of the low-frequency band gap is analyzed by using the sound pressure field, and the range of band gaps is calculated by using the finite element method and the spring-oscillator model. Although the research shows that the finite element calculation results are basically consistent with the theoretical calculation, there are still some errors, and the reasons for the errors are analyzed. Secondly, the finite element method and equivalent model method are used to explore the influence of parameters of the symmetric structure on the first band gap. The result shows that the upper limit of the first band gap decreases with the increase of the lattice constant and the wedge height and increases with the increase of the length of wedge base; the lower limit of the band gap decreases with the increase of the wedge height and length of wedge base and is independent of the change of lattice constant, which further reveals the essence of the band gap formation and verifies the accuracy of the equivalent model. This study provides some theoretical support for low-frequency noise control and broadens the design idea of symmetric phononic crystal.

Finite Element Analysis of a Phononic Crystal at Gigahertz Frequencies

2010 ◽  
Author(s):  
Seyedhamidreza Alaie ◽  
Arash K. Mousavi ◽  
Mehmet Su ◽  
Zayd C. Leseman
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Experimental Approach ◽  
Phononic Crystal ◽  
Experimental Results ◽  
Frequency Range ◽  
Element Analysis ◽  
Difference Time ◽  
Silicon Slab ◽  
Numerical Approaches

In this paper, the vibrational behavior of a phononic crystal is studied at gigahertz frequencies. The phononic crystal is comprised of a silicon slab with tungsten inclusions filtering out waves within the frequency range of 0.7 GHz to 1.1 GHz. Two-dimensional harmonic finite element analysis (FEA) is employed to model the transmission of stresswaves launched from a transmitter and passing through the crystal. The numerical results are compared with another prevalent numerical method, finite difference time domain (FDTD), as well as with experimental results. Comparisons made between the numerical approaches and experimental approach, show that the harmonic finite element analysis agrees well with experiment and potentially can explain the experimental results more precisely than FDTD. This more favorable comparison is attributed to a resonance that occurs between the transmitter and the phononic crystal.

The Calculation of the Band Structure in 3D Phononic Crystal with Hexagonal Lattice

2015 ◽  
Vol 70 (12) ◽  
pp. 979-983
Author(s):  
Mahrokh Aryadoust ◽  
H. Salehi
Keyword(s):  
Band Structure ◽  
Band Gap ◽  
Acoustic Waves ◽  
Phononic Crystal ◽  
Hexagonal Lattice ◽  
Three Dimensions ◽  
Elastic Band ◽  
Maximum Width ◽  
Filling Fraction ◽  
Irreducible Part

AbstractIn this article, the propagation of acoustic waves in the phononic crystals (PCs) of three dimensions with the hexagonal (HEX) lattice is studied theoretically. The PCs are constituted of nickel (Ni) spheres embedded in epoxy. The calculations of the band structure and the density of states are performed using the plane wave expansion (PWE) method in the irreducible part of the Brillouin zone (BZ). In this study, we analyse the dependence of the band structures inside (the complete band gap width) on c/a and filling fraction in the irreducible part of the first BZ. Also, we have analysed the band structure of the ALHA and MLHKM planes. The results show that the maximum width of absolute elastic band gap (AEBG) (0.045) in the irreducible part of the BZ of HEX lattice is formed for c/a=6 and filling fraction equal to 0.01. In addition, the maximum of the first and second AEBG widths are 0.0884 and 0.0474, respectively, in the MLHKM plane, and the maximum of the first and second AEBG widths are 0.0851 and 0.0431, respectively, in the ALHA plane.

scholarly journals Optimal Designs of Phononic Crystal Microstructures Considering Point and Line Defects

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 1993
Author(s):  
Jingjie He ◽  
Jiamei Sun ◽  
Juncheng Fan ◽  
Zhiyuan Jia ◽  
Xiaopeng Zhang
Keyword(s):  
Finite Element ◽  
Band Gap ◽  
Phononic Crystal ◽  
Hyperelliptic Curves ◽  
Unit Cell ◽  
Optimal Designs ◽  
Finite Element Models ◽  
Optimization Strategy ◽  
Unit Cells ◽  
Line Defects

In this paper, a two-stage optimization strategy for designing defective unit cells of phononic crystal (PnC) to explore the localization and waveguide states for target frequencies is proposed. In the optimization model, the PnC microstructures are parametrically described by a series of hyperelliptic curves, and the optimal designs can be obtained by systematically changing the designable parameters of hyperellipse. The optimization contains two individual processes. We obtain the configurations of a perfect unit cell for different orders of band gap maximization. Subsequently, by taking advantage of the supercell technique, the defective unit cells are designed based on the unit cell configuration for different orders of band gap maximization. The finite element models show the localization and waveguide phenomenon for target frequencies and validate the effectiveness of the optimal designs numerically.

Sign in / Sign up

Export Citation Format

Share Document