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

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 flexural and thickness-shear waves) in bicoupled 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), based 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 interference phenomenon. The ratios of band-coefficient 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 closed-form dispersion relation, 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.

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Formation of longitudinal wave band structures in one-dimensional phononic crystals

Journal of Applied Physics ◽

10.1063/1.3567911 ◽

2011 ◽

Vol 109 (7) ◽

pp. 073515 ◽

Cited By ~ 10

Author(s):

Y. Q. Guo ◽

D. N. Fang

Keyword(s):

Longitudinal Wave ◽

Phononic Crystals ◽

Wave Band ◽

Band Structures ◽

One Dimensional

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Elastic wave band gaps tuned by configuring radii of rods in two-dimensional phononic crystals with a hybrid square-like lattice

Modern Physics Letters B ◽

10.1142/s0217984915502425 ◽

2015 ◽

Vol 29 (35n36) ◽

pp. 1550242

Author(s):

Rongqiang Liu ◽

Haojiang Zhao ◽

Yingying Zhang ◽

Honghwei Guo ◽

Zongquan Deng

Keyword(s):

Plane Wave ◽

Elastic Wave ◽

Phononic Crystals ◽

Numerical Results ◽

Band Gaps ◽

Square Lattice ◽

Wave Band ◽

Two Dimensional ◽

Plane Wave Expansion ◽

Band Structures

The plane wave expansion (PWE) method is used to calculate the band gaps of two-dimensional (2D) phononic crystals (PCs) with a hybrid square-like (HSL) lattice. Band structures of both XY-mode and Z-mode are calculated. Numerical results show that the band gaps between any two bands could be maximized by altering the radius ratio of the inclusions at different positions. By comparing with square lattice and bathroom lattice, the HSL lattice is more efficient in creating larger gaps.

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Using coupling slabs to tailor surface-acoustic-wave band structures in phononic crystals consisting of pillars attached to elastic substrates

Science China Physics Mechanics and Astronomy ◽

10.1007/s11433-016-0395-6 ◽

2017 ◽

Vol 60 (4) ◽

Cited By ~ 4

Author(s):

Heng Zhang ◽

SiYuan Yu ◽

FuKang Liu ◽

Zhen Wang ◽

MingHui Lu ◽

...

Keyword(s):

Acoustic Wave ◽

Surface Acoustic Wave ◽

Phononic Crystals ◽

Wave Band ◽

Band Structures ◽

Elastic Substrates

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Low frequency phononic band structures in two-dimensional arc-shaped phononic crystals

Physics Letters A ◽

10.1016/j.physleta.2012.05.037 ◽

2012 ◽

Vol 376 (33) ◽

pp. 2256-2263 ◽

Cited By ~ 26

Author(s):

Zhenlong Xu ◽

Fugen Wu ◽

Zhongning Guo

Keyword(s):

Low Frequency ◽

Phononic Crystals ◽

Two Dimensional ◽

Band Structures

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“Fuzzy Band Gaps”: A Physically Motivated Indicator of Bloch Wave Evanescence in Phononic Systems

Crystals ◽

10.3390/cryst11010066 ◽

2021 ◽

Vol 11 (1) ◽

pp. 66

Author(s):

Connor D. Pierce ◽

Kathryn H. Matlack

Keyword(s):

Wave Propagation ◽

Dispersion Relation ◽

Quantitative Measure ◽

Bloch Wave ◽

Phononic Crystals ◽

Wave Transmission ◽

Band Gaps ◽

Dissipative Systems ◽

Frequency Range ◽

Wave Modes

Phononic crystals (PCs) have been widely reported to exhibit band gaps, which for non-dissipative systems are well defined from the dispersion relation as a frequency range in which no propagating (i.e., non-decaying) wave modes exist. However, the notion of a band gap is less clear in dissipative systems, as all wave modes exhibit attenuation. Various measures have been proposed to quantify the “evanescence” of frequency ranges and/or wave propagation directions, but these measures are not based on measurable physical quantities. Furthermore, in finite systems created by truncating a PC, wave propagation is strongly attenuated but not completely forbidden, and a quantitative measure that predicts wave transmission in a finite PC from the infinite dispersion relation is elusive. In this paper, we propose an “evanescence indicator” for PCs with 1D periodicity that relates the decay component of the Bloch wavevector to the transmitted wave amplitude through a finite PC. When plotted over a frequency range of interest, this indicator reveals frequency regions of strongly attenuated wave propagation, which are dubbed “fuzzy band gaps” due to the smooth (rather than abrupt) transition between evanescent and propagating wave characteristics. The indicator is capable of identifying polarized fuzzy band gaps, including fuzzy band gaps which exists with respect to “hybrid” polarizations which consist of multiple simultaneous polarizations. We validate the indicator using simulations and experiments of wave transmission through highly viscoelastic and finite phononic crystals.

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Elastic wave band gaps in 2D fractal phononic crystals

10.26678/abcm.cobem2021.cob2021-2336 ◽

2021 ◽

Author(s):

Victor Gustavo Ramos Costa Dos Santos ◽

Edson Jansen Pedrosa de Miranda Junior ◽

Jose Maria Campos dos Santos

Keyword(s):

Elastic Wave ◽

Phononic Crystals ◽

Band Gaps ◽

Wave Band

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Incorporating Compressional and Shear Wave Types Into Fuzzy Structure Models for Plates

Volume 3B: 15th Biennial Conference on Mechanical Vibration and Noise — Acoustics, Vibrations, and Rotating Machines ◽

10.1115/detc1995-0413 ◽

1995 ◽

Author(s):

Judith L. Rochat ◽

Victor W. Sparrow

Keyword(s):

Thin Plate ◽

Shear Waves ◽

Wave Theory ◽

Structure Theory ◽

Detailed Knowledge ◽

Bending Waves ◽

Incident Plane ◽

Dependent Mass ◽

Mass Spring ◽

Bending Wave

Abstract Although realistic complex structures are usually difficult to model theoretically, fuzzy structure theory enables one to produce such a model without a detailed knowledge of the entire structure. Using the theory established by Pierce et al. [A. D. Pierce, V. W. Sparrow, and D. A. Russell, J. Vib. Acoust. (to be published), also ASME 93-WA/NCA-17.] regarding fundamental structural-acoustic idealizations for structures with imprecisely known or fuzzy internals, the effects that fuzzy attachments have on different wave types in a primary (or master) structure are examined in this paper. In the theory by Pierce et al., the primary structure that undergoes vibrations is a thin plate mounted in an infinite baffle. On one side of the plate are fuzzy attachments, represented as an array of attached mass-spring-dashpot systems, which are excited by an incident plane pulse. This known theory explains the effects of these attachments on bending waves in the plate. In this paper, the theory is extended to isolated compressional and shear waves in a plate. While studying this new problem, it is discovered that coupling effects occur when the plate and attachment properties are not uniform in the direction perpendicular to the wave propagation. Hence, unlike the bending wave theory which models a finite thin plate with point attached oscillators, the new wave type theory uses a thin plate infinite in one direction with line attached oscillators also infinite in the same direction. For both the compressional and shear waves, it is found that the fuzzy attachments add an apparent frequency dependent mass and damping to the plate. These results are similar to those for the bending wave theory.

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Tunable Band Gaps of Acoustic Waves in Two-Dimensional Phononic Crystals With Reticular Band Structures

Volume 15: Sound, Vibration and Design ◽

10.1115/imece2009-13102 ◽

2009 ◽

Cited By ~ 1

Author(s):

Zi-Gui Huang ◽

Yunn-Lin Hwang ◽

Pei-Yu Wang ◽

Yen-Chieh Mao

Keyword(s):

Acoustic Waves ◽

Composite Structures ◽

Phononic Crystals ◽

Band Gaps ◽

Sound Insulation ◽

Two Dimensional ◽

The Finite Element Method ◽

Elastic Band ◽

Band Structures ◽

Elastic Band Gaps

The excellent applications and researches of so-called photonic crystals raise the exciting researches of phononic crystals. By the analogy between photon and phonon, repetitive composite structures that are made up of different elastic materials can also prevent elastic waves of some certain frequencies from passing by, i.e., the frequency band gap features also exist in acoustic waves. In this paper, we present the results of the tunable band gaps of acoustic waves in two-dimensional phononic crystals with reticular band structures using the finite element method. Band gaps variations of the bulk modes due to different thickness and angles of reticular band structures are calculated and discussed. The results show that the total elastic band gaps for mixed polarization modes can be enlarged or reduced by adjusting the orientation of the reticular band structures. The phenomena of band gaps of elastic or acoustic waves can potentially be utilized for vibration-free, high-precision mechanical systems, and sound insulation.

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