Boundary element method for band gap calculations of two-dimensional solid phononic crystals

Li, Fenglian; Wang, Yue-Sheng; Zhang, Chuanzeng; Yu, Gui‐Lan

doi:10.1016/j.enganabound.2012.10.003

Cited by 61 publications

(26 citation statements)

References 28 publications

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“…It requires only the discretization of the boundary and offers certain computational advantages over the domain discretization methods such as the FEM and FDTD method. The present authors have recently developed the BEM to compute the band structures of 2-D phononic crystals [20,21]. In the present paper, we will extend the BEM to calculate the elastic/acoustic wave transmission spectra of a phononic crystal strip.…”

Section: Introductionmentioning

confidence: 98%

Boundary element method for calculation of elastic wave transmission in two-dimensional phononic crystals

Wang

Zhang

2016

Sci. China Phys. Mech. Astron.

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A boundary element method (BEM) is presented to compute the transmission spectra of two-dimensional (2-D) phononic crystals of a square lattice which are finite along the x-direction and infinite along the y-direction. The cross sections of the scatterers may be circular or square. For a periodic cell, the boundary integral equations of the matrix and the scatterers are formulated. Substituting the periodic boundary conditions and the interface continuity conditions, a linear equation set is formed, from which the elastic wave transmission can be obtained. From the transmission spectra, the band gaps can be identified, which are compared with the band structures of the corresponding infinite systems. It is shown that generally the transmission spectra completely correspond to the band structures. In addition, the accuracy and the efficiency of the boundary element method are analyzed and discussed. phononic crystals, boundary element method, elastic wave transmission spectra PACS number(s): 43.

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Section: Introductionmentioning

confidence: 98%

Boundary element method for calculation of elastic wave transmission in two-dimensional phononic crystals

Wang

Zhang

2016

Sci. China Phys. Mech. Astron.

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“…The first approach has been successfully applied to compute the band gaps of 2D phononic crystals [4]. In the present work, the second approach, which does not require the formulation of BIEs on the boundary of the unit cell, is used for the analysis of normally incident plane longitudinal elastic waves on doubly periodic array of coplanar penny-shaped cracks.…”

Section: Introductionmentioning

confidence: 99%

“…The investigations of various kinds of periodic structures, such as phononic crystals and, especially, the elastic wave propagation in these structures, are of great importance due to their potential engineering applications [4,8,9]. In many cases, periodic systems of cracks can act as wave scatterers in periodic structures with generation of specific wave patterns due to their sharp edges.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Stresses Due to Time-Harmonic Elastic Wave Incidence on Doubly Periodic Array of Penny-Shaped Cracks

2014

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The symmetric frequency-domain problem of the interaction effects in rectangular lattice system of coplanar penny-shaped cracks located in an infinite elastic solid is numerically investigated. The problem is reduced to a boundary integral equation for the crack-opening-displacement in a unit cell by means of 3D periodic elastodynamic Green's function. This function is adopted for the effective calculation by its representation in the form of exponentially convergent Fourier integrals. A collocation method is used for the solution of the boundary integral equation. Numerical results for the mode-I dynamic stress intensity factor in the crack vicinities are obtained and analyzed depending on the wave number and the lattice size.

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“…BEM can handle almost arbitrarily shaped scatterers with a smaller number of unknowns, and is appropriate for wave scattering analysis in the infinite domains. The BEM method has studied the band structures of the two-dimensional phononic crystals [15]. In this paper we will extend BEM to compute the transmission response of three-phase phononic crystals, and discuss the accuracy of the method.…”

Section: Introductionmentioning

confidence: 99%

Transmission Calculation of Three-phase Phononic Crystals

Li¹

2017

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Boundary element method (BEM) is employed to compute the transmission of two-dimensional (2D) three-phase phononic crystals. The system is in a square lattice which has finite layers along the x-direction and is infinite along y-direction. The cross sections of the inclusions are circular. In a periodic unit cell, boundary integral equations of the matrix, the coating and the inclusion are given. A linear equation set is formed by substituting the periodic boundary conditions and the interface conditions, from which the transmission response can be obtained. Then the band gaps of the phononic system can be found. The obtained results are basically consistent with the band structures from the corresponding infinite systems. It is shown that the present method can accurately compute the transmission.

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Boundary element method for band gap calculations of two-dimensional solid phononic crystals

Cited by 61 publications

References 28 publications

Boundary element method for calculation of elastic wave transmission in two-dimensional phononic crystals

Boundary element method for calculation of elastic wave transmission in two-dimensional phononic crystals

Dynamic Stresses Due to Time-Harmonic Elastic Wave Incidence on Doubly Periodic Array of Penny-Shaped Cracks

Transmission Calculation of Three-phase Phononic Crystals

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