Flexural Wave Attenuation in a Multi-Frequency Locally Resonant Phononic Crystals Beam Resting on Elastic Foundations

A periodic bi-layer beam structure is proposed and the bandgap characteristic of flexural wave is studied in this paper. The single cell is made up of two bi-layer beams with four components. For the infinite structure, the flexural wave bandgap frequency algorithm is theoretically derived through Timoshenko beam theory, Hamilton principle, Bloch-Floquet theory and transfer matrix method. An analytical example is presented to illustrate the bandgap characteristic and FEA software simulation is conducted to demonstrate the validation of the algorithm. For the finite structure, the vibration transmission characteristic is studied with FEA software to show the flexural wave attenuation behavior of the periodic bi-layer beam. The results reveal that, the flexural wave is attenuated gradually in the stopband along the direction of wave propagation, while in the passband, it will propagate without attenuation. Comparisons with periodic single layer beam are studied to verify the convenience and flexibility of bi-layer beam. Finally, parametric influences on bandgaps are discussed, which will help the designers to make a better design for vibration reduction.

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Flexural wave attenuation in a sandwich beam with viscoelastic periodic cores

Journal of Sound and Vibration ◽

10.1016/j.jsv.2017.04.016 ◽

2017 ◽

Vol 400 ◽

pp. 227-247 ◽

Cited By ~ 6

Author(s):

Zhiwei Guo ◽

Meiping Sheng ◽

Jie Pan

Keyword(s):

Wave Attenuation ◽

Sandwich Beam ◽

Flexural Wave

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Flexural waves in elastically coupled telescopic metabeams

Journal of Vibration and Acoustics ◽

10.1115/1.4050809 ◽

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.

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Estimating formation shear attenuation from frequency-dependent dipole-flexural wave attenuation

10.1190/segam2017-17752126.1 ◽

2017 ◽

Author(s):

Qiaomu Qi ◽

Arthur Cheng ◽

Yunyue Elita Li

Keyword(s):

Wave Attenuation ◽

Flexural Wave ◽

Frequency Dependent

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Determination of formation shear attenuation from dipole sonic log data

Geophysics ◽

10.1190/geo2018-0006.1 ◽

2019 ◽

Vol 84 (3) ◽

pp. D73-D79 ◽

Cited By ~ 1

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.

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