The Influence of Viscosity on Band Gaps of 2D Phononic Crystal

Abstract

The influence of viscosity on band gaps of 2D phononic crystal is studied in this paper. The standard solid model is used to simulate the viscoelastic behavior of the host material. Cylindrical fillers embedded in the host are still assumed elastic material. The band gap problem of phononic crystal leads to a mathematical eigenvalue problem by using the plane wave expansion method and the Bloch-Floquet wave theory. An iterative algorithm is designed to obtain some wave bands due to the dependence of Lame coefficients on the frequency for the viscoelastic host. A numerical example is given for the steel/epoxy phononic crystal. Band gaps are evaluated for different viscoelastic parameters. It is found that the viscosity of host material affects not only the location but also the width of band gaps.

Keywords:

• phononic crystal
• band gap
• viscoelasticity
• plane wave expansion
• standard solid model

ACKNOWLEDGEMENT

This work is supported by The National Science Foundation of China (No. 10972029 and No. 10672019).