Flexural vibration band gaps of the multiple local resonance elastic metamaterial plates with irregular resonators

2019 ◽  
Vol 33 (33) ◽  
pp. 1950409
Author(s):  
Guo Li ◽  
Yake Dong ◽  
Genquan Li ◽  
Xuyan Liu ◽  
Chongnian Qu ◽  
...  
Keyword(s):  
Band Gap ◽  
Design Method ◽  
Influence Factors ◽  
Low Frequency ◽  
Flexural Vibration ◽  
Band Gaps ◽  
Geometrical Parameters ◽  
Vibration Band ◽  
Bending Vibration ◽  
Elastic Metamaterials

This paper presents the modeling technique, design method, a new working way and influence factors for elastic metamaterial plates. Two kinds of new elastic metamaterials plates with local resonators are designed. The band structure and transmission spectrum are calculated by finite element method (FEM). The formation mechanism of the bending vibration band gap is further analyzed by the displacement field of the band gap and the dynamic effective dislocation density of the metamaterial plate. Compared with regular shapes, irregular shapes of oscillators and rubber are easier to open bending band gaps. The effects of the geometrical parameters on the flexural vibration band gaps (FVBGs) are studied in detail. The related results can well confirm that the two novel types of local resonators illustrate the vibration characteristics of the two-degree-of-freedom system during the vibration, and two obvious FVBGs can be found in low frequency. The double-side metamaterial plates can broaden the width of FVBGs. The installation angles have no effect on the dispersion curves of the double-side metamaterial plates.

Band Gap Control in an Active Elastic Metamaterial With Negative Capacitance Piezoelectric Shunting

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
Y. Y. Chen ◽  
G. L. Huang ◽  
C. T. Sun
Keyword(s):  
Band Gap ◽  
Elastic Waves ◽  
Low Frequency ◽  
Lattice System ◽  
Band Gaps ◽  
Negative Capacitance ◽  
Bending Waves ◽  
Stiffness Constant ◽  
Elastic Metamaterials ◽  
Gap Control

Elastic metamaterials have been extensively investigated due to their significant effects on controlling propagation of elastic waves. One of the most interesting properties is the generation of band gaps, in which subwavelength elastic waves cannot propagate through. In the study, a new class of active elastic metamaterials with negative capacitance piezoelectric shunting is presented. We first investigated dispersion curves and band gap control of an active mass-in-mass lattice system. The unit cell of the mass-in-mass lattice system consists of the inner masses connected by active linear springs to represent negative capacitance piezoelectric shunting. It was demonstrated that the band gaps can be actively controlled and tuned by varying effective stiffness constant of the linear spring through appropriately selecting the value of negative capacitance. The promising application was then demonstrated in the active elastic metamaterial plate integrated with the negative capacitance shunted piezoelectric patches for band gap control of both the longitudinal and bending waves. It can be found that the location and the extent of the induced band gap of the elastic metamaterial can be effectively tuned by using shunted piezoelectric patch with different values of negative capacitance, especially for extremely low-frequency cases.

Flexural Vibration Band Gaps in a Ternary Phononic Crystal Thin Plate

2011 ◽  
Vol 675-677 ◽  
pp. 1085-1088
Author(s):  
Zong Jian Yao ◽  
Gui Lan Yu ◽  
Jian Bao Li
Keyword(s):  
Band Gap ◽  
Thin Plate ◽  
Mass Density ◽  
Phononic Crystal ◽  
Flexural Vibration ◽  
Expansion Method ◽  
Band Gaps ◽  
Physical Parameters ◽  
Vibration Band ◽  
Filling Fraction

The band structures of flexural waves in a ternary locally resonant phononic crystal thin plate are studied using the improved plane wave expansion method. And the thin concrete plate composed of a square array of steel cylinders hemmed around by rubber is considered here. Absolute band gaps of flexural vibration with low frequency are shown. The calculation results show that the band gap width is strongly dependent on the filling fraction, the radius ratio, the mass density and the Young’s modulus contrasts between the core and the coating. So by changing these physical parameters, the required band gap could be obtained.

Low-frequency and tuning characteristic of band gap in a symmetrical double-sided locally resonant phononic crystal plate with slit structure

2016 ◽  
Vol 30 (27) ◽  
pp. 1650203 ◽  
Author(s):  
X. P. Wang ◽  
P. Jiang ◽  
A. L. Song
Keyword(s):  
Band Gap ◽  
Power Transmission ◽  
Phononic Crystal ◽  
Low Frequency ◽  
Band Gaps ◽  
Geometrical Parameters ◽  
Band Frequency ◽  
Practical Applications ◽  
Tuning Characteristic ◽  
Lower Frequencies

In this paper, the low-frequency and tuning characteristic of band gap in a two-dimensional phononic crystal structure, consisting of a square array of aluminum cylindrical stubs deposited on both sides of a thin rubber plate with slit structure, are investigated. Using the finite element method, the dispersion relationships and power transmission spectra of this structure are calculated. In contrast to a typical phononic crystal without slit structure, the proposed slit structure shows band gaps at lower frequencies. The vibration modes of the band gap edges are analyzed to clarify the mechanism of the lowest band gaps. Additionally, the influence of the slit parameters and stub parameters on the band gaps in slit structure are investigated. The geometrical parameters of the slits and stubs were found to influence the band gaps; this is critical to understand for practical applications. These results will help in fabricating phononic crystal structures whose band frequency can be modulated at lower frequencies.

Evidence for complete low-frequency vibration band gaps in a thick elastic steel metamaterial plate

2019 ◽  
Vol 33 (04) ◽  
pp. 1950038 ◽  
Author(s):  
Suobin Li ◽  
Yihua Dou ◽  
Tianning Chen ◽  
Zhiguo Wan ◽  
Jingjing Huang ◽  
...  
Keyword(s):  
Band Gap ◽  
Steel Plate ◽  
Phononic Crystal ◽  
Low Frequency ◽  
Crystal Plate ◽  
Band Gaps ◽  
Formation Mechanisms ◽  
Vibration Band ◽  
Low Frequency Vibration ◽  
Thick Steel

Elastic steel metamaterial plates can be used for noise- and vibration-reduction due to unique physical properties related to their vibration band gap. However, obtaining a complete low-frequency vibration band gap in a thick elastic steel metamaterial plate is difficult. In this paper, we simulate a complete low-frequency vibration band gap in a thick elastic steel metamaterial plate. The structure consists of periodic, double-sided, composite stepped resonators, which were deposited on a 2D locally resonant phononic crystal plate. The phononic crystal plate consists of an array of rubber fillers embedded in a thick steel plate. The dispersion relations, power-transmission spectra, and the displacement fields of the eigenmodes are calculated using the finite-element method. The results show that, for the proposed structure, the opening of the first complete vibration band gap is reduced by a factor of 9.5 compared to a conventional thick elastic steel metamaterial plate. This causes attenuation of low-frequency elastic waves. The formation mechanisms for the vibration band gap are also explored numerically. The results indicate that the formation mechanism for the new low-frequency vibration band gap can be attributed to coupling between a local resonance mode of the composite stepped resonators and the Lamb wave mode of the thick steel-plate. The location of the vibration band gap is determined by the resonator mode of the composite stepped resonators. The vibration band gap effects of the composite stepped resonators are also investigated in this paper. We find that the location of the complete vibration band gaps can be modulated with a relatively low frequency using different composite stepped resonators. Such an elastic steel metamaterial plate with a complete low-frequency vibration band gap can be used to reduce both vibration and noise in various commercial and research applications.

scholarly journals Study on Tunable Band Gap of Flexural Vibration in a Phononic Crystals Beam with PBT

Crystals ◽  
2021 ◽  
Vol 11 (11) ◽  
pp. 1346
Author(s):  
Peng Zhao ◽  
Lili Yuan ◽  
Tingfeng Ma ◽  
Hanxing Wei
Keyword(s):  
Band Gap ◽  
Elastic Foundation ◽  
Vibration Isolation ◽  
Axial Stress ◽  
Low Frequency ◽  
Flexural Vibration ◽  
Phononic Crystals ◽  
Band Gaps ◽  
Response Curves ◽  
Element Method

Low-frequency flexural vibration plays a significant role in beam vibration control. To efficiently attenuate the propagation of flexural vibration at a low-frequency range, this paper proposes a new type of a phononic crystals beam with an adjustable band gap. The governing equations of flexural vibration in a periodic beam are established based on the Euler theory and Timoshenko theory. The band structures are calculated by the plane wave expansion method, the attenuation properties and transmission response curves with a finite periodic beam are calculated by the spectral element method and finite element method. The effects of the elastic foundation and axial stress on band gaps are discussed in detail, and the regulation of the temperature field on the band gap is emphatically studied. The theoretical and numerical results show that the elastic foundation and axial stress have significant influence on the band gap, and the location and width of the band gaps can be adjusted effectively when the Young’s modulus of PBT is changed by a varying temperature. The results are very useful for understanding and optimizing the design for composite vibration isolation beams.

Band-Gap Properties of Elastic Metamaterials With Inerter-Based Dynamic Vibration Absorbers

2018 ◽  
Vol 85 (7) ◽  
Author(s):  
Xiang Fang ◽  
Kuo-Chih Chuang ◽  
Xiaoling Jin ◽  
Zhilong Huang
Keyword(s):  
Band Gap ◽  
Frequency Band ◽  
Low Frequency ◽  
Lattice System ◽  
Band Gaps ◽  
Vibration Absorbers ◽  
Dynamic Vibration ◽  
Elastic Metamaterials ◽  
Dynamic Vibration Absorbers ◽  
Mass Spring

In this paper, inerter-based dynamic vibration absorbers (IDVAs) are applied in elastic metamaterials to broaden low-frequency band gaps. A discrete mass-spring lattice system and a distributed metamaterial beam carrying a periodic array of IDVAs are, respectively, considered. The IDVA consists of a spring and an inerter connected to a traditional mass-spring resonator. Compared to the traditional resonators, the special designed IDVAs generate two local-resonance (LR) band gaps for the discrete lattice system, a narrow low-frequency band gap and a wider high-frequency one. For the distributed IDVA-based metamaterial beam, in addition to the generated two separated LR band gaps, the Bragg band gap can also be significantly broadened and the three band gaps are very close to each other. Being able to amplify inertia, the IDVAs can be relatively light even operated for opening up low-frequency band gaps. When further introducing a dissipative damping mechanism into the IDVA-based metamaterials, the two close-split LR band gaps in the lattice system are merged into one wide band gap. As for the metamaterial beam with the dissipative IDVAs, an even wider band gap can be acquired due to the overlap of the adjacent LR and Bragg-scattering band gaps.

Flexural Vibration Band Gap in a Periodic Fluid-Conveying Pipe System Based on the Timoshenko Beam Theory

2011 ◽  
Vol 133 (1) ◽  
Author(s):  
Dianlong Yu ◽  
Jihong Wen ◽  
Honggang Zhao ◽  
Yaozong Liu ◽  
Xisen Wen
Keyword(s):  
Finite Element Method ◽  
Band Gap ◽  
Timoshenko Beam ◽  
Beam Theory ◽  
Flexural Vibration ◽  
Timoshenko Beam Theory ◽  
Flexural Wave ◽  
Vibration Band ◽  
Frequency Range ◽  
Pipe System

The flexural vibration band gap in a periodic fluid-conveying pipe system is studied based on the Timoshenko beam theory. The band structure of the flexural wave is calculated with a transfer matrix method to investigate the gap frequency range. The effects of the rotary inertia and shear deformation on the gap frequency range are considered. The frequency response of finite periodic pipe is calculated with a finite element method to validate the gap frequency ranges.

scholarly journals ACOUSTIC BAND GAP FORMATION IN METAMATERIALS

2010 ◽  
Vol 24 (25n26) ◽  
pp. 4935-4945 ◽  
Author(s):  
D. P. ELFORD ◽  
L. CHALMERS ◽  
F. KUSMARTSEV ◽  
G. M. SWALLOWE
Keyword(s):  
Band Gap ◽  
Lattice Constant ◽  
Low Frequency ◽  
Band Gaps ◽  
Gap Formation ◽  
Individual Band ◽  
Resonance Band ◽  
Frequency Regime ◽  
Sonic Crystal ◽  
The Individual

We present several new classes of metamaterials and/or locally resonant sonic crystal that are comprised of complex resonators. The proposed systems consist of multiple resonating inclusion that correspond to different excitation frequencies. This causes the formation of multiple overlapped resonance band gaps. We demonstrate theoretically and experimentally that the individual band gaps achieved, span a far greater range (≈ 2kHz) than previously reported cases. The position and width of the band gap is independent of the crystal's lattice constant and forms in the low frequency regime significantly below the conventional Bragg band gap. The broad envelope of individual resonance band gaps is attractive for sound proofing applications and furthermore the devices can be tailored to attenuate lower or higher frequency ranges, i.e., from seismic to ultrasonic.

Research on low-frequency band gap property of a hybrid phononic crystal

2018 ◽  
Vol 32 (15) ◽  
pp. 1850165 ◽  
Author(s):  
Yake Dong ◽  
Hong Yao ◽  
Jun Du ◽  
Jingbo Zhao ◽  
Ding Chao ◽  
...  
Keyword(s):  
Band Gap ◽  
Transmission Loss ◽  
Displacement Vector ◽  
Phononic Crystal ◽  
Influence Factors ◽  
Low Frequency ◽  
Bragg Scattering ◽  
The Finite Element Method ◽  
Flat Bands ◽  
Resonance Band

A hybrid phononic crystal has been investigated. The characteristic frequency of XY mode, transmission loss and displacement vector have been calculated by the finite element method. There are Bragg scattering band gap and local resonance band gap in the band structures. We studied the influence factors of band gap. There are many flat bands in the eigenfrequencies curve. There are many flat bands in the curve. The band gap covers a large range in low frequency. The band gaps cover more than 95% below 3000 Hz.

Sign in / Sign up

Export Citation Format

Share Document