TY - JOUR

T1 - Investigation of finite/infinite unidirectional elastic phononic plates by BEM

AU - Gao, Haifeng

AU - Matsumoto, Toshiro

AU - Takahashi, Toru

AU - Isakari, Hiroshi

N1 - Funding Information:
The authors are grateful to the financial support to this work by JSPS KAKENHI Grant Number 25289022 , the China Scholarship Council (CSC) No. 2009612004 , and Nagoya University .

PY - 2014/3

Y1 - 2014/3

N2 - The investigation of finite/infinite unidirectional elastic phononic plates is carried out by using the boundary element method (BEM). The transmissions of elastic waves in finite structures are calculated by solving a size-reduced system matrix, in which the transfer matrix formulated by BEM is used repeatedly and the unknown quantities on the free boundaries of cells are removed. For the infinite structures, the Bloch theorem is applied to the unit cell that has traction free boundaries, and the dispersion relation is plotted by extracting the eigenfrequencies of the nonlinear Bloch eigenvalue problem using a contour integral method. Furthermore, the eigenfrequencies of the finite structure are extracted by applying the contour integral method to the sized reduced system matrix, and a banded distribution of the eigenfrequencies is found. The correlation between the band structures of the infinite structures and the elastic wave transmission of the corresponding finite structures are presented. The frequency-banded nature exhibited by the finite structures shows a good agreement with the band structure of the corresponding infinite structures.

AB - The investigation of finite/infinite unidirectional elastic phononic plates is carried out by using the boundary element method (BEM). The transmissions of elastic waves in finite structures are calculated by solving a size-reduced system matrix, in which the transfer matrix formulated by BEM is used repeatedly and the unknown quantities on the free boundaries of cells are removed. For the infinite structures, the Bloch theorem is applied to the unit cell that has traction free boundaries, and the dispersion relation is plotted by extracting the eigenfrequencies of the nonlinear Bloch eigenvalue problem using a contour integral method. Furthermore, the eigenfrequencies of the finite structure are extracted by applying the contour integral method to the sized reduced system matrix, and a banded distribution of the eigenfrequencies is found. The correlation between the band structures of the infinite structures and the elastic wave transmission of the corresponding finite structures are presented. The frequency-banded nature exhibited by the finite structures shows a good agreement with the band structure of the corresponding infinite structures.

KW - Band structure

KW - Block Sakurai-Sugiura method

KW - Boundary element method

KW - Elastic waves

KW - Phononic plate

UR - http://www.scopus.com/inward/record.url?scp=84891507859&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84891507859&partnerID=8YFLogxK

U2 - 10.1016/j.enganabound.2013.12.003

DO - 10.1016/j.enganabound.2013.12.003

M3 - Article

AN - SCOPUS:84891507859

VL - 40

SP - 93

EP - 103

JO - Engineering Analysis with Boundary Elements

JF - Engineering Analysis with Boundary Elements

SN - 0955-7997

ER -