Study on band gap properties of two-dimensional phononic crystals based on generalized viscoelastic modeling

2019 ◽  
Vol 33 (32) ◽  
pp. 1950403
Author(s):  
Fengxiang Guo ◽  
Hui Guo ◽  
Pei Sun ◽  
Tao Yuan ◽  
Yansong Wang
Keyword(s):  
Plane Waves ◽  
Single Mode ◽  
Expansion Method ◽  
Maxwell Model ◽  
Phononic Crystals ◽  
Band Gaps ◽  
Two Dimensional ◽  
Band Structures ◽  
Material Parameters ◽  
Multi Mode

Viscoelastic materials can dissipate energy and hinder propagation for plane waves, which can adjust the band structures of phononic crystals (PCs). In this study, the wave propagation in a two-dimensional PC with a viscoelastic matrix is investigated. The Maxwell model is utilized to analyze the effect of material parameters on the frequency dependence of viscoelasticity. Material parameters include the relaxation time, the initial value and the final value of the shear modulus. Band structures of viscoelastic phononic crystals (VPCs) are solved by combining the plane wave expansion method and iterative algorithm based on Bloch theory. The effects of the viscoelasticity on the band structures are studied using the single-mode and multi-mode Maxwell models. Results reveal that the viscoelasticity of the materials not only extends the band gaps but also shifts the band gaps to lower frequencies. Furthermore, the viscoelasticity simulated by the multi-mode model can precisely adjust anyone of the band gaps of VPCs separately. Results provide insights into the design and applications of VPCs.

Tunable Band Gaps of Acoustic Waves in Two-Dimensional Phononic Crystals With Reticular Band Structures

2009 ◽  
Author(s):  
Zi-Gui Huang ◽  
Yunn-Lin Hwang ◽  
Pei-Yu Wang ◽  
Yen-Chieh Mao
Keyword(s):  
Acoustic Waves ◽  
Composite Structures ◽  
Phononic Crystals ◽  
Band Gaps ◽  
Sound Insulation ◽  
Two Dimensional ◽  
The Finite Element Method ◽  
Elastic Band ◽  
Band Structures ◽  
Elastic Band Gaps

The excellent applications and researches of so-called photonic crystals raise the exciting researches of phononic crystals. By the analogy between photon and phonon, repetitive composite structures that are made up of different elastic materials can also prevent elastic waves of some certain frequencies from passing by, i.e., the frequency band gap features also exist in acoustic waves. In this paper, we present the results of the tunable band gaps of acoustic waves in two-dimensional phononic crystals with reticular band structures using the finite element method. Band gaps variations of the bulk modes due to different thickness and angles of reticular band structures are calculated and discussed. The results show that the total elastic band gaps for mixed polarization modes can be enlarged or reduced by adjusting the orientation of the reticular band structures. The phenomena of band gaps of elastic or acoustic waves can potentially be utilized for vibration-free, high-precision mechanical systems, and sound insulation.

Effects of material parameters on the band gaps of two-dimensional three-component phononic crystals

2019 ◽  
Vol 125 (3) ◽  
Author(s):  
Chao Li ◽  
Linchang Miao ◽  
Quan You ◽  
Huanglei Fang ◽  
Xiaodong Liang ◽  
...  
Keyword(s):  
Phononic Crystals ◽  
Band Gaps ◽  
Two Dimensional ◽  
Material Parameters

Tuning Band Structures of Two-Dimensional Phononic Crystals With Biasing Fields

2014 ◽  
Vol 81 (9) ◽  
Author(s):  
Y. Huang ◽  
C. L. Zhang ◽  
W. Q. Chen
Keyword(s):  
Electric Field ◽  
Phononic Crystals ◽  
Band Gaps ◽  
Two Dimensional ◽  
Plane Wave Expansion ◽  
Band Structures ◽  
Biasing Fields ◽  
Small Fields ◽  
Electric Field Change ◽  
Repulsion Effect

The control of band structures of 2D phononic crystals (PCs) composed of piezoelectric inclusions and elastic isotropic matrix with mechanical/electrical biasing fields is theoretically investigated. The theory for small fields superposed on biasing fields and the plane wave expansion (PWE) method is employed to compute the band structures of the PCs under different biasing fields, including the initial shear/normal stress and the initial electric field. We find that the initial shear stress breaks the symmetry of the material. In consequence, the two bands associated with the level repulsion effect are opened near the apparent crosspoint and form a local band gap. On the other hand, the normal initial stress and the biasing electric field change the effective stiffness and shift the positions of band gaps. The observed phenomena show that the biasing fields can be flexibly used to tune the PC devices.

TUNABLE BAND STRUCTURES OF 2D MULTI-ATOM ARCHIMEDEAN-LIKE PHONONIC CRYSTALS

2012 ◽  
Vol 01 (02) ◽  
pp. 1250016 ◽  
Author(s):  
Y. L. XU ◽  
C. Q. CHEN ◽  
X. G. TIAN
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Phononic Crystal ◽  
Phononic Crystals ◽  
Band Gaps ◽  
Two Dimensional ◽  
Primitive Cell ◽  
The Finite Element Method ◽  
Band Structures ◽  
Solid System

Two dimensional multi-atom Archimedean-like phononic crystals (MAPCs) can be obtained by adding "atoms" at suitable positions in primitive cells of traditional simple lattices. Band structures of solid-solid and solid-air MAPCs are computed by the finite element method in conjunction with the Bloch theory. For the solid-solid system, our results show that the MAPCs can be suitably designed to split and shift band gaps of the corresponding traditional simple phononic crystal (i.e., with only one scatterer inside a primitive cell). For the solid-air system, the MAPCs have more and wider band gaps than the corresponding traditional simple phononic crystal. Numerical calculations for both solid-solid and solid-air MAPCs show that the band gap of traditional simple phononic crystal can be tuned by appropriately adding "atoms" into its primitive cell.

Bandgaps of Two-Dimensional Phononic Crystals With Sliding Interface Conditions

2014 ◽  
Vol 81 (6) ◽  
Author(s):  
Feng-Lian Li ◽  
Yue-Sheng Wang ◽  
Chuanzeng Zhang ◽  
Gui-Lan Yu
Keyword(s):  
Phononic Crystals ◽  
Interface Condition ◽  
Solid Matrix ◽  
Two Dimensional ◽  
Interface Conditions ◽  
Band Structures ◽  
Material Parameters ◽  
Sliding Interface ◽  
The Matrix ◽  
Dirichlet To Neumann Map

In the present paper, the Dirichlet-to-Neumann map method is employed to compute the band structures of two-dimensional phononic crystals with smoothly sliding connection conditions between the matrix and the scatterers, which are composed of square or triangular lattices of circular solid cylinders in a solid matrix. The solid/solid systems of various material parameters with sliding interface conditions are considered. The influence of sliding interface conditions on the band structures is analyzed and discussed. The results show that the smoothly sliding interface condition has significant effect on the band structure.

Elastic wave band gaps tuned by configuring radii of rods in two-dimensional phononic crystals with a hybrid square-like lattice

2015 ◽  
Vol 29 (35n36) ◽  
pp. 1550242
Author(s):  
Rongqiang Liu ◽  
Haojiang Zhao ◽  
Yingying Zhang ◽  
Honghwei Guo ◽  
Zongquan Deng
Keyword(s):  
Plane Wave ◽  
Elastic Wave ◽  
Phononic Crystals ◽  
Numerical Results ◽  
Band Gaps ◽  
Square Lattice ◽  
Wave Band ◽  
Two Dimensional ◽  
Plane Wave Expansion ◽  
Band Structures

The plane wave expansion (PWE) method is used to calculate the band gaps of two-dimensional (2D) phononic crystals (PCs) with a hybrid square-like (HSL) lattice. Band structures of both XY-mode and Z-mode are calculated. Numerical results show that the band gaps between any two bands could be maximized by altering the radius ratio of the inclusions at different positions. By comparing with square lattice and bathroom lattice, the HSL lattice is more efficient in creating larger gaps.

Flexural Vibration Band Gaps in Periodic Sandwich Beams With Auxetic Core

2007 ◽  
Author(s):  
Jihong Wen ◽  
Xisen Wen ◽  
Dianlong Yu
Keyword(s):  
Flexural Vibration ◽  
Expansion Method ◽  
Phononic Crystals ◽  
Band Gaps ◽  
Vibration Band ◽  
Sandwich Beams ◽  
Plane Wave Expansion ◽  
Plane Wave Expansion Method ◽  
One Dimensional ◽  
Material Parameters

The flexural vibration band gaps in one-dimensional periodic sandwich beams with auxetic core are studied basing on the theory of Phononic crystals. The band structures of one-dimensional periodic sandwich beams with auxetic core are presented with the plane wave expansion method, the regular calculation method in phononic crystals. Further, the effects of material parameters and structure parameters on the gaps are analyzed. The vibration band gaps in the sandwich beams provide a new idea for the vibration controlling of the structure.

Localization of In-Plane Guided Elastic Waves in a Two-Dimensional Solid Waveguiding Phononic Crystal

2011 ◽  
Vol 52-54 ◽  
pp. 1233-1236 ◽  
Author(s):  
A Li Chen ◽  
Yue Sheng Wang ◽  
Chuan Zeng Zhang
Keyword(s):  
Plane Wave ◽  
Guided Waves ◽  
Phononic Crystal ◽  
Expansion Method ◽  
Phononic Crystals ◽  
Two Dimensional ◽  
Plane Wave Expansion Method ◽  
Band Structures ◽  
Disorder Degree ◽  
Line Defects

Combined with the supercell technique, the plane wave expansion method is used to calculate the band structures for the in-plane wave of the two-dimensional solid-solid phononic crystals with line defects and the random disorders in either radius or location of the scatterers. The influences of the random disorders on the band structures and guided waves will be discussed. Propagation of the wave with one certain frequency in the waveguiding phononic crystals with different disorder degree is studied.

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