Flexural Wave Band Gaps in Phononic Crystal Euler-Bernoulli Beams Using Wave Finite Element and Plane Wave Expansion Methods

Miranda, Edson Jansen Pedrosa de; Santos, José Maria Campos dos

doi:10.1590/1980-5373-mr-2016-0877

Cited by 11 publications

(2 citation statements)

References 51 publications

(84 reference statements)

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“…There are two formation mechanisms of the elastic band gap in PCs: one is the Bragg scattering mechanism [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18], and the other is the locally resonant mechanism. The wave length corresponding to the elastic band gap formed by Bragg scattering is generally equal to the lattice size or lattice constant, which restricts its application in engineering practice.…”

Section: Introductionmentioning

confidence: 99%

A Numerical Method for Flexural Vibration Band Gaps in A Phononic Crystal Beam with Locally Resonant Oscillators

et al. 2019

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The differential quadrature method has been developed to calculate the elastic band gaps from the Bragg reflection mechanism in periodic structures efficiently and accurately. However, there have been no reports that this method has been successfully used to calculate the band gaps of locally resonant structures. This is because, in the process of using this method to calculate the band gaps of locally resonant structures, the non-linear term of frequency exists in the matrix equation, which makes it impossible to solve the dispersion relationship by using the conventional matrix-partitioning method. Hence, an accurate and efficient numerical method is proposed to calculate the flexural band gap of a locally resonant beam, with the aim of improving the calculation accuracy and computational efficiency. The proposed method is based on the differential quadrature method, an unconventional matrix-partitioning method, and a variable substitution method. A convergence study and validation indicate that the method has a fast convergence rate and good accuracy. In addition, compared with the plane wave expansion method and the finite element method, the present method demonstrates high accuracy and computational efficiency. Moreover, the parametric analysis shows that the width of the 1st band gap can be widened by increasing the mass ratio or the stiffness ratio or decreasing the lattice constant. One can decrease the lower edge of the 1st band gap by increasing the mass ratio or decreasing the stiffness ratio. The band gap frequency range calculated by the Timoshenko beam theory is lower than that calculated by the Euler-Bernoulli beam theory. The research results in this paper may provide a reference for the vibration reduction of beams in mechanical or civil engineering fields.

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Section: Introductionmentioning

confidence: 99%

A Numerical Method for Flexural Vibration Band Gaps in A Phononic Crystal Beam with Locally Resonant Oscillators

et al. 2019

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“…The main concern was the flexural wave/vibration in and frequency response of infinite/finite period beams. For periodic binary beams with two kind of materials: Lee et al [45] proposed a basis theory of bending wave propagation; Han et al [46] and Ni et al [47] introduced a modified transfer matrix method (MTM) by transforming the state parameters of TMM into four initial parameters based on EBT and TBT, respectively; Tao and Liao [48] investigated the effects of the clamped boundary condition and disturbance on the flexural wave propagation using the method of multiple reflections; de Miranda and Dos Santos [49] investigated theoretically using FEM, SEM, the wave finite element method (WFEM), the wave spectral element method (WSEM), the conventional and improved plane wave expansion (PWE) method and experimentally the forced response and band structure based on EBT. Cheng et al [50] investigated complex dispersion relations and the evanescent wave modes by their developed extended differential quadrature element method (EDQEM).…”

Section: Introductionmentioning

confidence: 99%

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

Guo

2018

Applied Sciences

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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.

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Computing dispersion diagrams and forced responses of arbitrarily varying waveguides

Ribeiro

Poggetto

Claeys

et al. 2023

International Journal of Mechanical Sciences

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Flexural Wave Band Gaps in Phononic Crystal Euler-Bernoulli Beams Using Wave Finite Element and Plane Wave Expansion Methods

Cited by 11 publications

References 51 publications

A Numerical Method for Flexural Vibration Band Gaps in A Phononic Crystal Beam with Locally Resonant Oscillators

A Numerical Method for Flexural Vibration Band Gaps in A Phononic Crystal Beam with Locally Resonant Oscillators

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

Computing dispersion diagrams and forced responses of arbitrarily varying waveguides

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