Flexural band gaps and response attenuation of periodic piping systems enhanced with localized and distributed resonators

AbstractNovel metamaterial concepts can be used to economically reduce flexural vibrations in coupled pipe-rack systems. Here, we model pipe on flexible supports as periodic systems and formulate dispersion relations using Floquet-Bloch theory which is verified by a finite element model. Owing to the flexibility of the coupled system, a narrow pass band is created in low frequency regime, in contrast to the case of pipe without any rack. Two types of vibration reduction mechanisms are investigated for pipe with different supports, i.e. simple and elastic support. In order to tune the band gap behaviour, lateral localized resonators are attached at the centre of each unit cell; conversely, the lateral distributed resonators are realized with a secondary pipe existing in the system. The results reveal that both Bragg and resonance type band gaps coexist in piping systems due to the presence of spatial periodicity and local resonance. Although, the response attenuation of a coupled pipe-rack system with distributed resonators is found to be little lower than the case with the localized one, the relatively low stiffness and damping values lead to cheaper solutions. Therefore, the proposed concept of distributed resonators represents a promising application in piping, power and process industries.

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ACOUSTIC BAND GAP FORMATION IN METAMATERIALS

International Journal of Modern Physics B ◽

10.1142/s0217979210057110 ◽

2010 ◽

Vol 24 (25n26) ◽

pp. 4935-4945 ◽

Cited By ~ 2

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.

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Magnetoelastic Coupling and Delta-E Effect in Magnetoelectric Torsion Mode Resonators

Sensors ◽

10.3390/s21062022 ◽

2021 ◽

Vol 21 (6) ◽

pp. 2022

Author(s):

Benjamin Spetzler ◽

Elizaveta V. Golubeva ◽

Ron-Marco Friedrich ◽

Sebastian Zabel ◽

Christine Kirchhof ◽

...

Keyword(s):

Low Frequency ◽

High Sensitivity ◽

Element Model ◽

Mode Number ◽

Frequency Change ◽

General Description ◽

Resonance Modes ◽

Field Sensor ◽

Magnetic Sensitivity ◽

Bending Modes

Magnetoelectric resonators have been studied for the detection of small amplitude and low frequency magnetic fields via the delta-E effect, mainly in fundamental bending or bulk resonance modes. Here, we present an experimental and theoretical investigation of magnetoelectric thin-film cantilevers that can be operated in bending modes (BMs) and torsion modes (TMs) as a magnetic field sensor. A magnetoelastic macrospin model is combined with an electromechanical finite element model and a general description of the delta-E effect of all stiffness tensor components Cij is derived. Simulations confirm quantitatively that the delta-E effect of the C66 component has the promising potential of significantly increasing the magnetic sensitivity and the maximum normalized frequency change ∆fr. However, the electrical excitation of TMs remains challenging and is found to significantly diminish the gain in sensitivity. Experiments reveal the dependency of the sensitivity and ∆fr of TMs on the mode number, which differs fundamentally from BMs and is well explained by our model. Because the contribution of C11 to the TMs increases with the mode number, the first-order TM yields the highest magnetic sensitivity. Overall, general insights are gained for the design of high-sensitivity delta-E effect sensors, as well as for frequency tunable devices based on the delta-E effect.

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Influence of Li2CO3 addition on electrical and magnetic properties of Ni0.6Mg0.4Fe2O4

Journal of Advanced Dielectrics ◽

10.1142/s2010135x20500034 ◽

2020 ◽

Vol 10 (03) ◽

pp. 2050003

Author(s):

M. R. Hassan ◽

M. T. Islam ◽

M. N. I. Khan

Keyword(s):

Magnetic Properties ◽

Single Phase ◽

Low Frequency ◽

Solid State Reaction Method ◽

Charge Carriers ◽

X Ray Diffraction ◽

X Ray ◽

Electrical And Magnetic Properties ◽

Frequency Regime ◽

Xrd Patterns

In this research, influence of adding Li2CO3 (at 0%, 2%, 4%, 6%) on electrical and magnetic properties of [Formula: see text][Formula: see text]Fe2O4 (with 60% Ni and 40% Mg) ferrite has been studied. The samples are prepared by solid state reaction method and sintered at 1300∘C for 6[Formula: see text]h. X-ray diffraction (XRD) patterns show the samples belong to single-phase cubic structure without any impurity phase. The magnetic properties (saturation magnetization and coercivity) of the samples have been investigated by VSM and found that the higher concentration of Li2CO3 reduces the hysteresis loss. DC resistivity increases with Li2CO3 contents whereas it decreases initially and then becomes constant at lower value with temperature which indicates that the studied samples are semiconductor. The dielectric dispersion occurs at a low-frequency regime and the loss peaks are formed in a higher frequency regime, which are due to the presence of resonance between applied frequency and hopping frequency of charge carriers. Notably, the loss peaks are shifted to the lower frequency with Li2CO3 additions.

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Locally resonant periodic structures with low-frequency band gaps

Journal of Applied Physics ◽

10.1063/1.4816052 ◽

2013 ◽

Vol 114 (3) ◽

pp. 033532 ◽

Cited By ~ 30

Author(s):

Zhibao Cheng ◽

Zhifei Shi ◽

Y. L. Mo ◽

Hongjun Xiang

Keyword(s):

Frequency Band ◽

Periodic Structures ◽

Low Frequency ◽

Band Gaps

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Design and optimization of acoustic liners with a shear grazing flow: OPAL software platform applications

INTER-NOISE and NOISE-CON Congress and Conference Proceedings ◽

10.3397/in-2021-1308 ◽

2021 ◽

Vol 263 (6) ◽

pp. 152-163

Author(s):

Remi Roncen ◽

Pierre Vuillemin ◽

Patricia Klotz ◽

Frank Simon ◽

Fabien Méry ◽

...

Keyword(s):

Noise Reduction ◽

Low Frequency ◽

Small Scale ◽

Software Platform ◽

Total Size ◽

Linearized Euler Equations ◽

Design And Optimization ◽

Acoustic Liners ◽

Frequency Regime ◽

Grazing Flow

In the context of noise reduction in diverse applications where a shear grazing flow is present (i.e., engine nacelle, jet pump, landing gear), improved acoustic liner solutions are being sought. This is particularly true in the low-frequency regime, where space constraints currently limit the efficiency of classic liner technology. To perform the required multi-objective optimization of complex meta-surface liner candidates, a software platform called OPAL was developed. Its first goal is to allow the user to assemble a large panel of parallel/serial assembly of unit acoustic elements, including the recent concept of LEONAR materials. Then, the physical properties of this liner can be optimized, relatively to given weighted objectives (noise reduction, total size of the sample, weight), for a given configuration. Alternatively, properties such as the different impedances of liner unit surfaces can be optimized. To accelerate the process, different nested levels of optimization are considered, from 0D analytical coarse designs in order to reduce the parameter space, up to 2D plan or axisymmetric high-order Discontinuous Galerkin resolution of the Linearized Euler Equations. The presentation will focus on the different aspects of liner design considered in OPAL, and present an application on different samples made for a small scale aeroacoustic bench.

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Effects on Pipe Vibrations of Cavitation in an Orifice and in Globe-Style Valves

Volume 9: 6th FSI, AE and FIV and N Symposium ◽

10.1115/pvp2006-icpvt-11-93882 ◽

2006 ◽

Cited By ~ 2

Author(s):

Se´bastien Caillaud ◽

Rene´-Jean Gibert ◽

Pierre Moussou ◽

Joe¨l Cohen ◽

Fabien Millet

Keyword(s):

Nuclear Power ◽

Power Plants ◽

Low Frequency ◽

Flow Regimes ◽

Piping System ◽

Low Frequencies ◽

Choked Flow ◽

Single Hole ◽

Piping Systems ◽

Large Amplitude Vibrations

A piping system of French nuclear power plants displays large amplitude vibrations in particular flow regimes. These troubles are attributed to cavitation generated by single-hole orifices in depressurized flow regimes. Real scale experiments on high pressure test rigs and on-site tests are then conducted to explain the observed phenomenon and to find a solution to reduce pipe vibrations. The first objective of the present paper is to analyze cavitation-induced vibrations in the single-hole orifice. It is then shown that the orifice operates in choked flow with supercavitation, which is characterized by a large unstable vapor pocket. One way to reduce pipe vibrations consists in suppressing the orifices and in modifying the control valves. Three technologies involving a standard trim and anti-cavitation trims are tested. The second objective of the paper is to analyze cavitation-induced vibrations in globe-style valves. Cavitating valves operate in choked flow as the orifice. Nevertheless, no vapor pocket appears inside the pipe and no unstable phenomenon is observed. The comparison with an anti-cavitation solution shows that cavitation reduction has no impact on low frequency excitation. The effect of cavitation reduction on pipe vibrations, which involve essentially low frequencies, is then limited and the first solution, which is the standard globe-style valve installed on-site, leads to acceptable pipe vibrations. Finally, this case study may have consequences on the design of piping systems. First, cavitation in orifices must be limited. Choked flow in orifices may lead to supercavitation, which is here a damaging and unstable phenomenon. The second conclusion is that the reduction of cavitation in globe-style valve in choked flow does not reduce pipe vibrations. The issue is then to limit cavitation erosion of valve trims.

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Vibration Characteristics of Metamaterial Beams With Periodic Local Resonances

Journal of Vibration and Acoustics ◽

10.1115/1.4028453 ◽

2014 ◽

Vol 136 (6) ◽

Cited By ~ 53

Author(s):

M. Nouh ◽

O. Aldraihem ◽

A. Baz

Keyword(s):

Band Gap ◽

Low Frequency ◽

Element Model ◽

Small Mass ◽

Vibration Characteristics ◽

Structural Vibrations ◽

Low Frequencies ◽

Theoretical Predictions ◽

Gap Characteristics ◽

Unique Band

Vibration characteristics of metamaterial beams manufactured of assemblies of periodic cells with built-in local resonances are presented. Each cell consists of a base structure provided with cavities filled by a viscoelastic membrane that supports a small mass to form a source of local resonance. This class of metamaterial structures exhibits unique band gap behavior extending to very low-frequency ranges. A finite element model (FEM) is developed to predict the modal, frequency response, and band gap characteristics of different configurations of the metamaterial beams. The model is exercised to demonstrate the band gap and mechanical filtering capabilities of this class of metamaterial beams. The predictions of the FEM are validated experimentally when the beams are subjected to excitations ranging between 10 and 5000 Hz. It is observed that there is excellent agreement between the theoretical predictions and the experimental results for plain beams, beams with cavities, and beams with cavities provided with local resonant sources. The obtained results emphasize the potential of the metamaterial beams for providing significant vibration attenuation and exhibiting band gaps extending to low frequencies. Such characteristics indicate that metamaterial beams are more effective in attenuating and filtering low-frequency structural vibrations than plain periodic beams of similar size and weight.

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Spacecraft and interplanetary contributions to the magnetic environment on-board LISA Pathfinder

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/staa830 ◽

2020 ◽

Vol 494 (2) ◽

pp. 3014-3027

Author(s):

M Armano ◽

H Audley ◽

J Baird ◽

P Binetruy ◽

M Born ◽

...

Keyword(s):

Magnetic Field ◽

New Technologies ◽

Magnetic Measurements ◽

Magnetic Measurement ◽

Low Frequency ◽

Lisa Pathfinder ◽

Frequency Regime ◽

The Magnetic Field ◽

Instrument Sensitivity ◽

Stationary Component

ABSTRACT LISA Pathfinder (LPF) has been a space-based mission designed to test new technologies that will be required for a gravitational wave observatory in space. Magnetically driven forces play a key role in the instrument sensitivity in the low-frequency regime (mHz and below), the measurement band of interest for a space-based observatory. The magnetic field can couple to the magnetic susceptibility and remanent magnetic moment from the test masses and disturb them from their geodesic movement. LPF carried on-board a dedicated magnetic measurement subsystem with noise levels of 10 $\rm nT \ Hz^{-1/2}$ from 1 Hz down to 1 mHz. In this paper we report on the magnetic measurements throughout LPF operations. We characterize the magnetic environment within the spacecraft, study the time evolution of the magnetic field and its stability down to 20 μHz, where we measure values around 200 $\rm nT \ Hz^{-1/2}$, and identify two different frequency regimes, one related to the interplanetary magnetic field and the other to the magnetic field originating inside the spacecraft. Finally, we characterize the non-stationary component of the fluctuations of the magnetic field below the mHz and relate them to the dynamics of the solar wind.

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Phononic Band Gaps of Elastic Periodic Structures: A Homogenization Theory Study

Volume 10: Mechanics of Solids and Structures, Parts A and B ◽

10.1115/imece2007-43969 ◽

2007 ◽

Author(s):

Ying-Hong Liu ◽

Chien C. Chang ◽

Ruey-Lin Chern ◽

C. Chung Chang

Keyword(s):

Elastic Constants ◽

Periodic Structures ◽

Mass Density ◽

Density Ratio ◽

Low Frequency ◽

Phononic Crystals ◽

Band Gaps ◽

Homogenization Theory ◽

Dominant Factor ◽

Phononic Band Gaps

In this study, we investigate band structures of phononic crystals with particular emphasis on the effects of the mass density ratio and of the contrast of elastic constants. The phononic crystals consist of arrays of different media embedded in a rubber or epoxy. It is shown that the density ratio rather than the contrast of elastic constants is the dominant factor that opens up phononic band gaps. The physical background of this observation is explained by applying the theory of homogenization to investigate the group velocities of the low-frequency bands at the center of symmetry Γ.

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