Elastic Metamaterials With Low-Frequency Passbands Based on Lattice System With On-Site Potential

2016 ◽  
Vol 138 (2) ◽  
Author(s):  
Yongquan Liu ◽  
Xiaohui Shen ◽  
Xianyue Su ◽  
C. T. Sun
Keyword(s):  
Elastic Waves ◽  
Present Method ◽  
Wave Attenuation ◽  
Low Frequency ◽  
Lattice System ◽  
Two Dimensional ◽  
High Frequencies ◽  
Elastic Metamaterials

An elastic metamaterial with a low-frequency passband is proposed by imitating a lattice system with linear on-site potential. It is shown that waves can only propagate in the tunable passband. Then, two kinds of elastic metamaterials with double passbands are designed. Great wave attenuation performance can be obtained at frequencies between the two passbands for locally resonant type metamaterials, and at both low and high frequencies for the diatomic type metamaterials. Finally, the strategy to design two-dimensional (2D) metamaterials is demonstrated. The present method can be used to design new types of small-size waveguides, filters, and other devices for elastic waves.

scholarly journals Numerical Modelling and Optimization of Two-Dimensional Phononic Band Gaps in Elastic Metamaterials with Square Inclusions

2021 ◽  
Vol 11 (7) ◽  
pp. 3124
Author(s):  
Alya Alhammadi ◽  
Jin-You Lu ◽  
Mahra Almheiri ◽  
Fatima Alzaabi ◽  
Zineb Matouk ◽  
...  
Keyword(s):  
Elastic Wave ◽  
Tungsten Carbide ◽  
Composite Structure ◽  
Elastic Waves ◽  
Wave Attenuation ◽  
Low Frequency ◽  
Filling Fraction ◽  
Carbide Composite ◽  
Elastic Metamaterials ◽  
Tungsten Carbide Composite

A numerical simulation study on elastic wave propagation of a phononic composite structure consisting of epoxy and tungsten carbide is presented for low-frequency elastic wave attenuation applications. The calculated dispersion curves of the epoxy/tungsten carbide composite show that the propagation of elastic waves is prohibited inside the periodic structure over a frequency range. To achieve a wide bandgap, the elastic composite structure can be optimized by changing its dimensions and arrangement, including size, number, and rotation angle of square inclusions. The simulation results show that increasing the number of inclusions and the filling fraction of the unit cell significantly broaden the phononic bandgap compared to other geometric tunings. Additionally, a nonmonotonic relationship between the bandwidth and filling fraction of the composite was found, and this relationship results from spacing among inclusions and inclusion sizes causing different effects on Bragg scatterings and localized resonances of elastic waves. Moreover, the calculated transmission spectra of the epoxy/tungsten carbide composite structure verify its low-frequency bandgap behavior.

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.

The finite-product method in the theory of waves and stability

2009 ◽  
Vol 466 (2114) ◽  
pp. 471-491 ◽  
Author(s):  
C. J. Chapman ◽  
S. V. Sorokin
Keyword(s):  
Dispersion Relation ◽  
Elastic Waves ◽  
Low Frequency ◽  
Wave Theory ◽  
Finite Product ◽  
High Frequencies ◽  
Polynomial Approximations ◽  
Wide Range ◽  
Product Method ◽  
Finite Products

This paper presents a method of analysing the dispersion relation and field shape of any type of wave field for which the dispersion relation is transcendental. The method involves replacing each transcendental term in the dispersion relation by a finite-product polynomial. The finite products chosen must be consistent with the low-frequency, low-wavenumber limit; but the method is nevertheless accurate up to high frequencies and high wavenumbers. Full details of the method are presented for a non-trivial example, that of anti-symmetric elastic waves in a layer; the method gives a sequence of polynomial approximations to the dispersion relation of extraordinary accuracy over an enormous range of frequencies and wavenumbers. It is proved that the method is accurate because certain gamma-function expressions, which occur as ratios of transcendental terms to finite products, largely cancel out, nullifying Runge’s phenomenon. The polynomial approximations, which are unrelated to Taylor series, introduce no spurious branches into the dispersion relation, and are ideal for numerical computation. The method is potentially useful for a very wide range of problems in wave theory and stability theory.

scholarly journals Vortex-type elastic structured media and dynamic shielding

2012 ◽  
Vol 468 (2146) ◽  
pp. 3027-3046 ◽  
Author(s):  
M. Brun ◽  
I. S. Jones ◽  
A. B. Movchan
Keyword(s):  
Elastic Waves ◽  
Continuous Medium ◽  
Lattice System ◽  
Periodic Lattice ◽  
Two Dimensional ◽  
Metamaterial Structure ◽  
Structured Media ◽  
Analytical Work

The paper presents an approach to modelling a novel elastic metamaterial structure that possesses non-trivial dispersion features. A system of spinners has been embedded into a two-dimensional periodic lattice system. The analysis of the motion of the spinners is used to derive an expression for a ‘chiral term’ in the equations describing the dynamics of the lattice. Dispersion of elastic waves is shown to possess innovative filtering and polarization properties induced by the vortex-type nature of the structured media. The related effective behaviour in a continuous medium is implemented to build a shielding cloak around an obstacle. Analytical work is accompanied by numerical illustrations.

Wave Manipulation of Two-Dimensional Periodic Lattice by Parametric Excitation

2019 ◽  
Vol 87 (1) ◽  
Author(s):  
Xiao-Dong Yang ◽  
Qing-Dian Cui ◽  
Wei Zhang
Keyword(s):  
Parametric Excitation ◽  
Elastic Waves ◽  
High Frequency ◽  
Low Frequency ◽  
Waveguide Structure ◽  
Phononic Crystals ◽  
Periodic Lattice ◽  
Two Dimensional ◽  
Time Dynamic ◽  
Mechanical Waves

Abstract Phononic crystals composed of delicately designed periodic units are used to control spatial and spectral properties of acoustic or elastic waves. The ability to manipulate transmitting waves in a real-time dynamic manner provides a new concept in programable phononic crystals and metamaterials. In this study, the mechanical waves and bandgaps in a two-dimensional spring-mass array loaded by high-frequency parametric excitation have been investigated by both analytical and numerical methods. It is found that the high-frequency parametric excitation provides an equivalent additional stiffness which leads to low-frequency bandgaps. By tuning the parametric excitation, the versatility of such a dynamic modulating technique has been presented. The waveguide structure has also been designed and studied by non-uniformly distributed parametric excitations.

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.

A Novel Fault-location Method for HVDC Transmission Lines Based on Concentric Relaxation Principle and Wavelet Packet

2020 ◽  
Vol 13 (5) ◽  
pp. 705-716
Author(s):  
Congshan Li ◽  
Ping He ◽  
Feng Wang ◽  
Cunxiang Yang ◽  
Yukun Tao ◽  
...  
Keyword(s):  
Transmission Lines ◽  
Traveling Wave ◽  
Fault Location ◽  
Wave Attenuation ◽  
Wavelet Packet ◽  
Low Frequency ◽  
Evaluation Process ◽  
Location Method ◽  
Hvdc Transmission ◽  
Instantaneous Energy

Background: A novel fault location method of HVDC transmission line based on a concentric relaxation principle is proposed in this paper. Methods: Due to the different position of fault, the instantaneous energy measured from rectifier and inverter are different, and the ratio k between them is the relationship to the fault location d. Through the analysis of amplitude-frequency characteristics, we found that the wave attenuation characteristic of low frequency in the traveling wave is stable, and the amplitude of energy is larger, so we get the instantaneous energy ratio by using the low-frequency data. By using the method of wavelet packet decomposition, the voltage traveling wave signal was decomposed. Results: Finally, calculate the value k. By using the data fitting, the relative function of k and d can be got, that is the fault location function. Conclusion: After an exhaustive evaluation process considering different fault locations, fault resistances, and noise on the unipolar DC transmission system, four-machine two-area AC/DC parallel system, and an actual complex grid, the method presented here showed a very accurate and robust behavior.

Despeckling of Sar Images Using Shrinkage of Two-Dimensional Discrete Orthonormal S-Transform

2020 ◽  
pp. 2150023
Author(s):  
Priya R. Kamath ◽  
Kedarnath Senapati ◽  
P. Jidesh
Keyword(s):  
High Frequency ◽  
Low Frequency ◽  
Relevant Information ◽  
Detection Algorithm ◽  
Two Dimensional ◽  
Sar Images ◽  
S Transform ◽  
Processing Step ◽  
Frequency Components ◽  
Shock Filter

Speckles are inherent to SAR. They hide and undermine several relevant information contained in the SAR images. In this paper, a despeckling algorithm using the shrinkage of two-dimensional discrete orthonormal S-transform (2D-DOST) coefficients in the transform domain along with shock filter is proposed. Also, an attempt has been made as a post-processing step to preserve the edges and other details while removing the speckle. The proposed strategy involves decomposing the SAR image into low and high-frequency components and processing them separately. A shock filter is used to smooth out the small variations in low-frequency components, and the high-frequency components are treated with a shrinkage of 2D-DOST coefficients. The edges, for enhancement, are detected using a ratio-based edge detection algorithm. The proposed method is tested, verified, and compared with some well-known models on C-band and X-band SAR images. A detailed experimental analysis is illustrated.

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