Band Structure in Carbon Nanostructure Phononic Crystals

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

doi:10.1590/1980-5373-mr-2016-0898

Cited by 20 publications

(1 citation statement)

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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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