Bandgap calculations of two-dimensional solid–fluid phononic crystals with the boundary element method

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

doi:10.1016/j.wavemoti.2012.12.001

Cited by 58 publications

(41 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…and (b) show the profiles of the system of a square lattice with the elastic waves propagating along the two high symmetry directions, GX and GM directions, respectively. Here we define GX and GM directions by following the first Brillouin zone [20,21]. In this paper, the solid/solid and solid/fluid systems are investigated.…”

Section: Problem Formulationmentioning

confidence: 99%

“…In the following, we take the systems in ref. [21] as the examples and adopt the same material parameters.…”

Section: Transmission Spectra For Solid/fluid Systemsmentioning

confidence: 99%

“…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: 99%

“…Transmission spectra in the iron/water system with a square lattice: (a) for the GM direction, (c) for the GX direction; and (b) for the band structures computed by the BEM[21].…”

mentioning

confidence: 99%

See 3 more Smart Citations

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

Wang

Zhang

2016

Sci. China Phys. Mech. Astron.

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Problem Formulationmentioning

confidence: 99%

“…In the following, we take the systems in ref. [21] as the examples and adopt the same material parameters.…”

Section: Transmission Spectra For Solid/fluid Systemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Transmission spectra in the iron/water system with a square lattice: (a) for the GM direction, (c) for the GX direction; and (b) for the band structures computed by the BEM[21].…”

mentioning

confidence: 99%

See 2 more Smart Citations

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

Wang

Zhang

2016

Sci. China Phys. Mech. Astron.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Barnett and Greengard [23,24] used the quasi-periodic Green's function to formulate the boundary integral equations. Recently, Li et al [25][26][27] developed an easier BEM to calculate the band structure of solid/solid and solid/liquid phononic crystals, in their method, a fundamental solution with periodic nature is employed, and then a linear eigenvalue equation is obtained based on the periodic boundary conditions. The purpose of this paper is to investigate the effect of interface imperfection on the wave propagation behavior in solid/solid phononic crystals.…”

Section: Introductionmentioning

confidence: 99%

Investigation of phononic band gap structures considering interface effects

Zhu

Zhong

Sun

et al. 2014

Physica B: Condensed Matter

View full text Add to dashboard Cite

A matrix‐exponential decomposition‐based time‐domain method for band structure calculation of one‐dimensional periodic structures

Wang

Zhang

et al. 2016

Int J Numerical Modelling

Self Cite

View full text Add to dashboard Cite

SUMMARYA time-domain method for calculating the band structure of one-dimensional periodic structures is proposed. During the time-stepping of the method, the column vector containing the spatially sampled field data is updated by multiplying with an iteration matrix. The iteration matrix is first obtained by using the matrix-exponential decomposition technique. Then, the small nonzero elements of the matrix are pruned to improve its sparse structure, so that the efficiency of the matrix-vector multiplication involved in each time-step is enhanced. The numerical results show that the method is conditionally stable but is much more stable than the conventional finitedifference time-domain (FDTD) method. The time-step with which the method runs stably can be much larger than the Courant-Friedrichs-Lewy (CFL) limit. And moreover, the method is found to be particularly efficient for the band structure calculation of large-scale structures containing a defect with a very high wave speed, where the conventional FDTD method may generally lose its efficiency severely. For this kind of structures, not only the stability requirement can be significantly relaxed, but also the matrix-pruning operation can be very effectively performed. In the numerical experiments for large-scale quasi-periodic phononic crystal structures containing a defect layer, significantly higher efficiency than the conventional FDTD method can be achieved by the proposed method without an evident accuracy deterioration if the wave speed of the defect layer is relatively high.

show abstract

Bandgap calculations of two-dimensional solid–fluid phononic crystals with the boundary element method

Cited by 58 publications

References 27 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

Investigation of phononic band gap structures considering interface effects

A matrix‐exponential decomposition‐based time‐domain method for band structure calculation of one‐dimensional periodic structures

Contact Info

Product

Resources

About