scholarly journals Optimization of a type of elastic metamaterial for broadband wave suppression

2021 ◽  
Vol 477 (2251) ◽  
pp. 20210337
Author(s):  
Kun Wu ◽  
Haiyan Hu ◽  
Lifeng Wang
Keyword(s):  
Vibration Isolation ◽  
Wave Attenuation ◽  
Low Frequency ◽  
Dispersion Analysis ◽  
Mass Unit ◽  
Super Cell ◽  
Unit Cells ◽  
Sequential Quadratic Programming Method ◽  
Continuous Frequency ◽  
Quadratic Programming Method

The optimal design is studied for a type of one-dimensional dissipative metamaterial to achieve broadband wave attenuation at low-frequency ranges. The complex dispersion analysis is made on a super-cell consisting of multiple mass-in-mass unit cells. An optimization algorithm based on the sequential quadratic programming method is used to design the wave suppression of target frequencies by coupling multiple separate narrow bandgaps into a broad bandgap. A new objective function is proposed in the optimization process for a continuous bandgap. Then, the continuous frequency range with low-wave transmissibility is optimized to achieve the maximal width of bandgap. The stiffness optimization of super-cell gives the broad bandgap from 10 Hz to 22.9 Hz at low-frequency ranges. In addition, numerical simulations are conducted for a type of dissipative metamaterial composed of a finite number of periodicities. The level of vibration isolation can be tuned by adjusting a critical value in the optimization scheme. The wave suppression in the numerical simulation well coincides with the obtained bandgaps and verifies the optimization results.

Origami-Based Bistable Metastructures for Low-Frequency Vibration Control

2021 ◽  
Vol 88 (5) ◽  
Author(s):  
Mingkai Zhang ◽  
Jinkyu Yang ◽  
Rui Zhu
Keyword(s):  
Vibration Isolation ◽  
Energy Analysis ◽  
Geometrical Nonlinearity ◽  
Low Frequency ◽  
Quantitative Relationship ◽  
Vibration Modes ◽  
Two Dimensional ◽  
Low Frequency Vibration ◽  
Dynamic Experiments ◽  
Unit Cells

Abstract In this research, we aim to combine origami units with vibration-filtering metastructures. By employing the bistable origami structure as resonant unit cells, we propose metastructures with low-frequency vibration isolation ability. The geometrical nonlinearity of the origami building block is harnessed for the adjustable stiffness of the metastructure’s resonant unit. The quantitative relationship between the overall stiffness and geometric parameter of the origami unit is revealed through the potential energy analysis. Both static and dynamic experiments are conducted on the bistable origami cell and the constructed beam-like metastructure to verify the adjustable stiffness and the tunable vibration isolation zone, respectively. Finally, a two-dimensional (2D) plate-like metastructure is designed and numerically studied for the control of different vibration modes. The proposed origami-based metastructures can be potentially useful in various engineering applications where structures with vibration isolation abilities are appreciated.

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.

Effects of “Finiteness” on Wave Propagation and Vibration in Elastic Periodic Structures

Aerospace ◽  
2004 ◽  
Author(s):  
Mahmoud I. Hussein ◽  
Gregory M. Hulbert ◽  
Richard A. Scott
Keyword(s):  
Frequency Band ◽  
Vibration Isolation ◽  
Wave Attenuation ◽  
Periodic Structures ◽  
Stop Band ◽  
Forced Response ◽  
Band Frequency ◽  
Mode Localization ◽  
Unit Cells ◽  
Frequency Behavior

The dynamics of finite elastic periodically layered structures is compared to that of the constituent periodic media. The focus is on both the frequency behavior and the spatial response. Through simulations of harmonically induced wave motion within a finite number of unit cells, the frequency band structure and attenuation characteristics of infinite and finite periodic systems are shown to conform under certain conditions. It is concluded that only one or two unit cells of a periodic material are required for “frequency bandness” to carry through to a finite structure, and only three to four unit cells are necessary for significant wave attenuation to take place when the structure is excited at a stop-band frequency. Furthermore, vibration analyses are conducted on a bounded fully periodic structure. The natural frequency spread is shown to conform with the frequency band layout of the infinite periodic material, and the steady-state forced response is observed to exhibit mode localization patterns that resemble those of the infinite periodic medium. These results could be used for setting guidelines for the design of periodic structures for vibration isolation and frequency filtering.

Vibration isolation characteristics of finite periodic tetra-chiral lattice coating filled with internal resonators

2016 ◽  
Vol 230 (16) ◽  
pp. 2840-2850 ◽  
Author(s):  
Dawei Zhu ◽  
Xiuchang Huang ◽  
Hongxing Hua ◽  
Hui Zheng
Keyword(s):  
Band Gap ◽  
Vibration Isolation ◽  
Periodic Structures ◽  
Low Frequency ◽  
Band Gaps ◽  
Stiffened Plate ◽  
Frequency Range ◽  
Vibration Attenuation ◽  
Unit Cells ◽  
Internal Resonators

Owing to their locally resonant mechanism, internal resonators are usually used to provide band gaps in low-frequency region for many types of periodic structures. In this study, internal resonators are used to improve the vibration attenuation ability of finite periodic tetra-chiral coating, enabling high reduction of the radiated sound power by a vibrating stiffened plate. Based on the Bloch theorem and finite element method, the band gap characteristics of tetra-chiral unit cells filled with and without internal resonators are analysed and compared to reveal the relationship between band gaps and vibration modes of such tetra-chiral unit cells. The rotational vibration of internal resonators can effectively strengthen the vibration attenuation ability of tetra-chiral lattice and extend the effective frequency range of vibration attenuation. Two tetra-chiral lattices with and without internal resonators are respectively designed and their vibration transmissibilities are measured using the hammering method. The experimental results confirm the vibration isolation effect of the internal resonators on the finite periodic tetra-chiral lattice. The tetra-chiral lattice as an acoustic coating is applied to a stiffened plate, and analysis results indicate that the internal resonators can obviously enhance the vibration attenuation ability of tetra-chiral lattice coating in the frequency range of the band gap corresponding to the rotating vibration mode of internal resonators. When the soft rubber with the internal resonators in tetra-chiral layers has gradient elastic modulus, the vibration attenuation ability and noise reduction of the tetra-chiral lattice coating are basically enhanced in the frequency range of the corresponding band gaps of tetra-chiral unit cells.

Coupled Piezoelectric Phononic Crystal for Adaptive Broadband Wave Attenuation by Destructive Interference

2020 ◽  
Vol 87 (9) ◽  
Author(s):  
Jiawen Xu ◽  
Xin Zhang ◽  
Ruqiang Yan
Keyword(s):  
Phase Difference ◽  
Wave Attenuation ◽  
Phononic Crystal ◽  
Low Frequency ◽  
Crystal Plate ◽  
Destructive Interference ◽  
Negative Capacitance ◽  
Frequency Range ◽  
Frequency Wave ◽  
Unit Cells

Abstract In this paper, we report a piezoelectric phononic crystal plate featuring broadband wave attenuation. In the piezoelectric phononic crystal system, the transmitted elastic wave is attenuated owing to destructive interference by taking advantages of phase difference. The proposed concept is applied to a piezoelectric phononic crystal plate synthesized by functional dual-lane units that yields phase difference. Whereas, the piezoelectric unit-cells are connected negative capacitance shunt circuits individually. Our analysis shows that the coupled phononic crystal has a strong broadband low-frequency wave attenuation capability. The bandwidth of 10 dB wave attenuation is broadened by 34 times in the vicinity of 5 kHz comparing to that of a local resonance metamaterial under the same mechanical configuration. Moreover, the frequency range of wave attenuation of the proposed system can be online adjusted through the modification of the external shunt circuits.

Modeling and Analysis of Phononic Crystal With Coupled Lanes for Enhanced Elastic Wave Attenuation

2020 ◽  
Vol 143 (2) ◽  
Author(s):  
Jiawen Xu ◽  
Guobiao Hu ◽  
Lihua Tang ◽  
Yumin Zhang ◽  
Ruqiang Yan
Keyword(s):  
Elastic Wave ◽  
Phase Difference ◽  
Wave Attenuation ◽  
Phononic Crystal ◽  
Low Frequency ◽  
Fem Analysis ◽  
Phononic Crystals ◽  
Attractive Potential ◽  
Destructive Interference ◽  
Unit Cells

Abstract Phononic crystals and metamaterials have attractive potential in elastic wave attenuation and guiding over specific frequency ranges. Different from traditional phononic crystals/metamaterials consisting of identical unit cells, a phononic crystal with coupled lanes is reported in this article for enhanced elastic wave attenuation in the low-frequency regime. The proposed phononic crystal takes advantages of destructive interference mechanism. A finitely length phononic crystal plate consisting of coupled lanes is considered for conceptual verification. The coupled lanes are designed to split the incident elastic wave into separated parts with a phase difference to produce destructive interference. Theoretical modeling and finite element method (FEM) analysis are presented. It is illustrated that significant elastic wave attenuation is realized when the phase difference of elastic waves propagating through the coupled lanes approximates π. Besides, multiple valleys in the transmission can be achieved in a broad frequency range with one at a frequency as low as 1.85 kHz with unit cells’ width and length of 25 mm and ten unit cells in one lane.

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 Rheology of rounded mammalian cells over continuous high-frequencies

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Gotthold Fläschner ◽  
Cosmin I. Roman ◽  
Nico Strohmeyer ◽  
David Martinez-Martin ◽  
Daniel J. Müller
Keyword(s):  
High Frequency ◽  
Mammalian Cells ◽  
Mechanical Response ◽  
Cell Mass ◽  
Low Frequency ◽  
Mass Measurements ◽  
High Frequencies ◽  
Polymer Relaxation ◽  
Continuous Frequency ◽  
Rheological Experiments

AbstractUnderstanding the viscoelastic properties of living cells and their relation to cell state and morphology remains challenging. Low-frequency mechanical perturbations have contributed considerably to the understanding, yet higher frequencies promise to elucidate the link between cellular and molecular properties, such as polymer relaxation and monomer reaction kinetics. Here, we introduce an assay, that uses an actuated microcantilever to confine a single, rounded cell on a second microcantilever, which measures the cell mechanical response across a continuous frequency range ≈ 1–40 kHz. Cell mass measurements and optical microscopy are co-implemented. The fast, high-frequency measurements are applied to rheologically monitor cellular stiffening. We find that the rheology of rounded HeLa cells obeys a cytoskeleton-dependent power-law, similar to spread cells. Cell size and viscoelasticity are uncorrelated, which contrasts an assumption based on the Laplace law. Together with the presented theory of mechanical de-embedding, our assay is generally applicable to other rheological experiments.

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.

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