Metastructures with double-spiral resonators for low-frequency flexural wave attenuation

2021 ◽  
Vol 130 (1) ◽  
pp. 014901
Author(s):  
Jung-San Chen ◽  
Tzung-Yu Chen ◽  
Yu-Chi Chang
Keyword(s):  
Wave Attenuation ◽  
Low Frequency ◽  
Flexural Wave ◽  
Double Spiral

Flexural waves in elastically coupled telescopic metabeams

2021 ◽  
pp. 1-28
Author(s):  
Rajan Prasad ◽  
Arnab Banerjee
Keyword(s):  
Wave Propagation ◽  
Band Gap ◽  
Wave Attenuation ◽  
Dynamic Stiffness ◽  
Equations Of Motion ◽  
Low Frequency ◽  
Length Ratio ◽  
Beam Equation ◽  
Flexural Wave ◽  
Constitutive Components

Abstract This paper investigates the flexural wave propagation through elastically coupled metabeams. It is assumed that the metabeam is formed by connecting successive beams with each other using distributed elastic springs. The equations of motion of a representative unit of the above mentioned novel structural form is established by dividing it into three constitutive components that are two side beams, modeled employing Euler-Bernoulli beam equation and an elastically coupled articulated distributed spring connection (ECADSC) at middle. ECADSC is modeled as parallel double beams connected by distributed springs. The underlying mechanics of this system in context of elastic wave propagation is unique when compared with the existing state of art in which local resonators, inertial amplifiers etc. are attached to the beam to widen the attenuation bandwidth. The dynamic stiffness matrix is employed in conjunction with Bloch-Floquet theorem to derive the band-structure of the system. It is identified that the coupling coefficient of the distributed spring layer and length ratio between the side beams and the elastic coupling plays the key role in the wave attenuation. It has been perceived that a considerable widening of the attenuation band gap in the low-frequency can be achieved while the elastically distributed springs are weak and distributed in a small stretch. Specifically, 140% normalized band gap can be obtained only by tuning the stiffness and the length ratio without adding any added masses or resonators to the structure.

Determination of formation shear attenuation from dipole sonic log data

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. D73-D79 ◽  
Author(s):  
Qiaomu Qi ◽  
Arthur C. H. Cheng ◽  
Yunyue Elita Li
Keyword(s):  
Reservoir Characterization ◽  
Wave Attenuation ◽  
Synthetic Data ◽  
Low Frequency ◽  
P Wave ◽  
Flexural Wave ◽  
S Wave ◽  
Additional Energy ◽  
Log Data ◽  
Sonic Log

ABSTRACT Formation S-wave attenuation, when combined with compressional attenuation, serves as a potential hydrocarbon indicator for seismic reservoir characterization. Sonic flexural wave measurements provide a direct means for obtaining the in situ S-wave attenuation at log scale. The key characteristic of the flexural wave is that it propagates at the formation shear slowness and experiences shear attenuation at low frequency. However, in a fast formation, the dipole log consists of refracted P- and S-waves in addition to the flexural wave. The refracted P-wave arrives early and can be removed from the dipole waveforms through time windowing. However, the refracted S-wave, which is often embedded in the flexural wave packet, is difficult to separate from the dipole waveforms. The additional energy loss associated with the refracted S-wave results in the estimated dipole attenuation being higher than the shear attenuation at low frequency. To address this issue, we have developed a new method for accurately determining the formation shear attenuation from the dipole sonic log data. The method uses a multifrequency inversion of the frequency-dependent flexural wave attenuation based on energy partitioning. We first developed our method using synthetic data. Application to field data results in a shear attenuation log that is consistent with lithologic interpretation of other available logs.

Low-frequency flexural wave attenuation in metamaterial sandwich beam with hourglass lattice truss core

Wave Motion ◽  
2021 ◽  
pp. 102750
Author(s):  
Zhenkun Guo ◽  
Guobiao Hu ◽  
Vladislav Sorokin ◽  
Lihua Tang ◽  
Xiaodong Yang ◽  
...  
Keyword(s):  
Wave Attenuation ◽  
Sandwich Beam ◽  
Low Frequency ◽  
Flexural Wave ◽  
Truss Core

Broadband Wave Attenuation in Locally Resonant Periodic Flexural Beams With Force-Moment Resonators

2013 ◽  
Author(s):  
Michael Y. Wang ◽  
Xiaoming Wang
Keyword(s):  
Degrees Of Freedom ◽  
Wave Attenuation ◽  
Low Frequency ◽  
Flexural Wave ◽  
Frequency Range ◽  
Resonant Structures ◽  
Force Moment ◽  
Flexural Wave Propagation ◽  
Bloch’S Theorem ◽  
Attenuation Characteristics

We investigate flexural wave propagation in Euler-Bernoulli beams with periodically suspended 2-DOF force-moment resonators. We use the transfer matrix method for a unit cell in the beam in conjunction with Bloch’s theorem, to define the dispersion curves and frequency band structure. Our analysis shows that the uncoupled force-moment resonators generate rich attenuation properties that are not observed in the conventional locally resonant structures with suspended force-only (or moment-only) vibrators. As a prime focus, we identify a Bragg-like band gap below the resonance frequency of the resonator and its coupling with the resonance gap, giving rise to a potentially super-wide attenuation gap that can be tuned for any low frequency range. The analysis presented can be extended to other types of phononic meta-materials and structures of multi-degrees of freedom (and distributed) resonators, which may exhibit more practically significant wave attenuation characteristics.

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.

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.

A waveform inversion technique for measuring elastic wave attenuation in cylindrical bars

Geophysics ◽  
1992 ◽  
Vol 57 (6) ◽  
pp. 854-859 ◽  
Author(s):  
Xiao Ming Tang
Keyword(s):  
Elastic Wave ◽  
Wave Attenuation ◽  
Waveform Inversion ◽  
Finite Size ◽  
Low Frequency ◽  
Frequency Range ◽  
Multiple Reflections ◽  
Low Frequencies ◽  
The Time Domain ◽  
Attenuation Values

A new technique for measuring elastic wave attenuation in the frequency range of 10–150 kHz consists of measuring low‐frequency waveforms using two cylindrical bars of the same material but of different lengths. The attenuation is obtained through two steps. In the first, the waveform measured within the shorter bar is propagated to the length of the longer bar, and the distortion of the waveform due to the dispersion effect of the cylindrical waveguide is compensated. The second step is the inversion for the attenuation or Q of the bar material by minimizing the difference between the waveform propagated from the shorter bar and the waveform measured within the longer bar. The waveform inversion is performed in the time domain, and the waveforms can be appropriately truncated to avoid multiple reflections due to the finite size of the (shorter) sample, allowing attenuation to be measured at long wavelengths or low frequencies. The frequency range in which this technique operates fills the gap between the resonant bar measurement (∼10 kHz) and ultrasonic measurement (∼100–1000 kHz). By using the technique, attenuation values in a PVC (a highly attenuative) material and in Sierra White granite were measured in the frequency range of 40–140 kHz. The obtained attenuation values for the two materials are found to be reliable and consistent.

Tunable Nonlinear Band Gaps in a Sandwich-Like Meta-Plate

2021 ◽  
Author(s):  
Yu Xue ◽  
Jinqiang Li ◽  
Yu Wang ◽  
Fengming Li
Keyword(s):  
Band Gap ◽  
Vibration Suppression ◽  
Wave Attenuation ◽  
Structural Parameters ◽  
Low Frequency ◽  
Dispersion Analysis ◽  
Response Analysis ◽  
Working Mechanism ◽  
Frequency Wave ◽  
The Galerkin Method

Abstract This paper aims to explore the actual working mechanism of sandwich-like meta-plates by periodically attaching nonlinear mass-beam-spring (MBS) resonators for low-frequency wave absorption. The nonlinear MBS resonator consists of a mass, a cantilever beam and a spring that can provide negative stiffness in the transverse vibration of the resonator, and its stiffness is tunable by changing the parameters of the spring. Considering the nonlinear stiffness of the resonator, the energy method is applied to obtain the dispersion relation of the sandwich-like meta-plate and the band-gap bounds related to the amplitude of resonator is derived by dispersion analysis. For the finite sized sandwich-like meta-plate with the fully free boundary condition subjected to external excitations, its dynamic equation is also established by the Galerkin method. The frequency response analysis of the meta-plate is carried out by the numerical simulation, whose band-gap range demonstrates good agreement with the theoretical one. Results show that the band-gap range of the present meta-plate is tunable by the design of the structural parameters of the MBS resonator. Furthermore, by analyzing the vibration suppression of the finite sized meta-plate, it can be observed that the nonlinearity of resonators can widen the wave attenuation range of meta-plate.

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