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S tudy on the convergence of plane wave expansion method in calculation the band structure of one dimensional typical phononic crystal

ZHI QIANG NI1,* , ZI MING ZHANG1, LIN HAN1, YAN ZHANG1

Affiliation

  1. College of Mechanics and Materials, Hohai University, Nanjing 210098, People’s Republic of China

Abstract

We study the convergence of plane wave expansion method (PWEM) while calculating the band structure of one dimensional typical phononic crystals by taking the example of Euler Bernoulli beam. The both algebraic formats of th e conventional and improved PWEM (CPWEM and IPWEM) were derived from the dynamic differential equation. The convergence of the PWEM was analyzed through the low and high eigen frequencies of highly symmetric points. The numerical experiment shows that the IPWEM has better convergence, which is very efficient to calculate the band structure of one dimensional typical phononic crystal systems of large elastic mismatch in searching for large band gaps..

Keywords

One dimensional typical phononic crystals Euler Bernoulli beam Plane wave expansion method, Convergence.

Citation

ZHI QIANG NI, ZI MING ZHANG, LIN HAN, YAN ZHANG, S tudy on the convergence of plane wave expansion method in calculation the band structure of one dimensional typical phononic crystal, Optoelectronics and Advanced Materials - Rapid Communications, 6, 1-2, January-February 2012, pp.87-90 (2012).

Submitted at: Nov. 15, 2011

Accepted at: Feb. 20, 2012