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.

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.

Study on the Band Gap and its Influencing Factors for one Dimensional Phononic Crystal

2011 ◽  
Vol 121-126 ◽  
pp. 448-452
Author(s):  
Yu Yang He ◽  
Xiao Xiong Jin
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Band Gap ◽  
Cross Section ◽  
Phononic Crystal ◽  
Filling Rate ◽  
Lumped Mass ◽  
Height Ratio ◽  
One Dimensional ◽  
Lumped Mass Method

The width of band gap is calculated with lumped mass method in order to study the wave propagation of longitudinal and transverse elastic wave of one-dimensional phononic crystal. The starting and terminating frequency is analyzed by changing the filling rate, the density difference of two materials, cross-section height ratio, and the Young's modulus of the scatter.

scholarly journals Generalized Multiscale Finite Element Method for Elastic Wave Propagation in the Frequency Domain

Computation ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 63 ◽  
Author(s):  
Uygulana Gavrilieva ◽  
Maria Vasilyeva ◽  
Eric T. Chung
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Propagation ◽  
Elastic Wave ◽  
Coarse Grid ◽  
Basis Functions ◽  
Interface Conditions ◽  
Multiscale Finite Element Method ◽  
Multiscale Finite Element ◽  
Element Method

In this work, we consider elastic wave propagation in fractured media. The mathematical model is described by the Helmholtz problem related to wave propagation with specific interface conditions (Linear Slip Model, LSM) on the fracture in the frequency domain. For the numerical solution, we construct a fine grid that resolves all fracture interfaces on the grid level and construct approximation using a finite element method. We use a discontinuous Galerkin method for the approximation by space that helps to weakly impose interface conditions on fractures. Such approximation leads to a large system of equations and is computationally expensive. In this work, we construct a coarse grid approximation for an effective solution using the Generalized Multiscale Finite Element Method (GMsFEM). We construct and compare two types of the multiscale methods—Continuous Galerkin Generalized Multiscale Finite Element Method (CG-GMsFEM) and Discontinuous Galerkin Generalized Multiscale Finite Element Method (DG-GMsFEM). Multiscale basis functions are constructed by solving local spectral problems in each local domains to extract dominant modes of the local solution. In CG-GMsFEM, we construct continuous multiscale basis functions that are defined in the local domains associated with the coarse grid node and contain four coarse grid cells for the structured quadratic coarse grid. The multiscale basis functions in DG-GMsFEM are discontinuous and defined in each coarse grid cell. The results of the numerical solution for the two-dimensional Helmholtz equation are presented for CG-GMsFEM and DG-GMsFEM for different numbers of multiscale basis functions.

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.

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.

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