Design guidelines for flexural wave attenuation of slender beams with local resonators

Liu, Yaozong; Yu, Dianlong; Li, Li; Zhao, Honggang; Wen, Jihong; Wen, Xisen

doi:10.1016/j.physleta.2006.10.056

Cited by 93 publications

(57 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The main concerns have been the band gaps and frequency responses of bending waves caused by Bragg scattering and locally resonant in infinite/finite periodic beams. For periodic beams with single DOF (degree-of-freedom) resonators: Yu et al [34] and Liu et al [35] analyzed the complex band structures using the transfer matrix method (TMM) based on TBT and EBT, respectively. Yu et al [34] further analyzed the frequency response function (FRF, i.e., transmission) using the FEM and validated the results by experiments.…”

Section: Introductionmentioning

confidence: 99%

“…Yu et al [34] further analyzed the frequency response function (FRF, i.e., transmission) using the FEM and validated the results by experiments. Liu et al [35] further analyzed the FRF using TMM, particularly concerning the influence of different local resonators, and summarized some design guidelines for this kind of structure. Xiao et al [36] analyzed the complex band structures by the spectral element method (SEM) and examined the effects of various system parameters on band-gap behavior.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Reverberation-Ray Matrix Analysis and Interpretation of Bending Waves in Bi-Coupled Periodic Multi-Component Beams

Guo

2018

Applied Sciences

View full text Add to dashboard Cite

Featured Application: The method of reverberation-ray matrix (MRRM) and the interpretation of bending waves proposed in this paper provide respectively analysis method and profound knowledge for bending waves in bi-coupled periodic multi-component beams. These achievements will push forward the applications of bi-coupled periodic multi-component beams in wave filtering and vibration isolation.Abstract: Most existing research on periodic beams concerns bending waves in mono-coupled and bi-coupled periodic mono-component beams with the unit cell containing only one beam segment, and very few works on bi-coupled periodic multi-component beams with the unit cell containing more than one beam segments study the bending waves in structures with only binary unit cells. This paper presents the method of reverberation-ray matrix (MRRM) as an alternative theoretical method for analyzing the dispersion characteristics of bending waves with the wavelength greater than the size of the cross-sections of all components in bi-coupled periodic multi-component beams. The formulation of MRRM is proposed in detail with its numerically well-conditioned property being emphasized, which is validated through comparison of the results obtained with the counterpart results by other methods for exemplified bi-coupled periodic beams. Numerical examples are also provided to illustrate the comprehensive dispersion curves represented as the relations between any two among three in frequency, wavenumber (wavelength) and phase-velocity for summarizing the general features of the dispersion characteristics of bending waves in bi-coupled periodic multi-component beams. The effects of the geometrical and material parameters of constituent beams and the unit-cell configuration on the band structures are also demonstrated by numerical examples. The most innovative finding indicated from the dispersion curves is that the frequencies corresponding to the Brillouin zone boundary may not be the demarcation between the pass-band and stop-band for bending waves in bi-coupled periodic multi-component beams.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Reverberation-Ray Matrix Analysis and Interpretation of Bending Waves in Bi-Coupled Periodic Multi-Component Beams

Guo

2018

Applied Sciences

View full text Add to dashboard Cite

show abstract

“…Thirdly, bending waves in bicoupled periodic beams consisting of a uniform beam and periodically attached local resonators (LRs) bearing LR bandgaps have been studied for various types of resonators and beams. For LR periodic beams with single degree-of-freedom (DOF) resonators, Liu et al [34] and Yu et al [35] researched the complex band structures and the frequency response functions (FRFs) theoretically and experimentally, respectively based on Euler-Bernoulli beam theoi^ and Timoshenko beam theory. For LR periodic Euler-Bernoulli beams with two DOF resonators, Yu et al [36] analyzed the complex band structures, the FRFs, and the characteristic modes, which were validated by experimental FRFs.…”

Section: Introductionmentioning

confidence: 99%

Formation of Bending-Wave Band Structures in Bicoupled Beam-Type Phononic Crystals

Guo

Fang

2013

Journal of Applied Mechanics

View full text Add to dashboard Cite

Beam-type phononic crystals as one kind of periodic material bear frequency bands for bending waves. For the first time, this paper presents formation mechanisms of the phase constant spectra in pass-bands of bending waves (coupled fiexural and thickness-shear waves) in bicoupied beam-type phononic crystals based on the model of periodic binary beam with rigidly connected joints. Closed-form dispersion relation of bending waves in the bicoupled periodic binary beam is obtained by our proposed method of reverberation-ray matrix (MRRM), ba.ied on which the bending-wave band structures in the bicoupled binary beam phononic crystal are found to be generated from the dispersion curves of the equivalent bending waves in the unit cell due to the zone folding effect, the cut-off characteristic of thickness-shear wave mode, and the wave inteiference phenomenon. The ratios of band-coejficient products, the characteristic times of the unit cell and the characteristic times of the constituent beams are revealed as the three kinds of essential parameters deciding the formation of bending-wave band structures. The MRRM, the dosed-form dispersion reiation, the formation mechanisms, and the essential parameters for the bending-wave band structures in bicoupled binary beam phononic crystals are validated by numerical examples, all of which will promote the applications of beam-type phononic crystals for wave filtering/guiding and vibration isolation/control.

show abstract

“…In recent studies, metamaterial beams, shafts and rods endowed with periodic resonators have been investigated. In order to filter undesired longitudinal 17 , flexural [18][19][20][21][22][23][24][25][26] or torsional 27,28 waves, a periodic structure can be equipped with resonator units that entail new band gaps different from those produced by Bragg scattering 7 . The introduction of damping devices in such resonator units contributes to energy dissipation, thereby reducing vibration amplitude 29 .…”

mentioning

confidence: 99%

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

Iqbal

Jaya

Bursi

et al. 2020

Sci Rep

View full text Add to dashboard Cite

Novel metamaterial concepts can be used to economically reduce flexural vibrations in coupled piperack 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. Pipes conveying fluid supported in equally spaced racks are very common in liquefied natural gas (LNG) plants, thermal power plants, petroleum industries, chemical plants and in many other engineering applications. LNG plant consists of many units such as gas receiving terminals, pipelines, storage tanks, etc. Long pipelines in such plants are used to carry refrigerated liquefied gas to storage tanks and shipping terminals. Excessive vibrations of pipelines due to ambient load, flow pulsation, valve or support excitation can result in fatigue damage, loosening of connections, etc., which may lead to fire, explosion, safety and environmental issues. It is thus essential to protect them from large vibration amplitude. To crystallize the idea, an LNG plant containing a coupled pipe-rack system connected to a tank 1 is shown in Fig. 1a. Such a system usually contains pipes of different dimensions supported on a finite periodic rack as highlighted in Fig. 1b. Periodic structures have been used as a common tool for mitigation of acoustic and elastic waves over the past decades 2-5. Periodicity in a structure may be in one, two or in all the three dimensions 6. Such systems exhibit unique frequency band gap characteristics 3 , which can be generated either due to the Bragg scattering 6,7 or by local resonances 8. As a result, they allow only waves of a certain frequencies to pass through, which are represented as pass or propagation bands. The remaining frequencies get attenuated, thereby forming stop or non-propagation bands. If the spatial periodicity of a structure is comparable to the wavelength λ, then Bragg band gaps are induced in the structure and appear around the frequencies governed by the Bragg condition = = … λ () l n n , where...

show abstract

Design guidelines for flexural wave attenuation of slender beams with local resonators

Cited by 93 publications

References 16 publications

Reverberation-Ray Matrix Analysis and Interpretation of Bending Waves in Bi-Coupled Periodic Multi-Component Beams

Reverberation-Ray Matrix Analysis and Interpretation of Bending Waves in Bi-Coupled Periodic Multi-Component Beams

Formation of Bending-Wave Band Structures in Bicoupled Beam-Type Phononic Crystals

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

Contact Info

Product

Resources

About