Abstract: The one dimensional plane wave expansion (PWE) algorithm is improved using iterative method in order to solve the problem of nonlinear changing of elastic constants with frequency, which is found in calculating of the band gaps of one dimensional viscoelastic phononic crystals. The new method is applied in the research of the vibration band gap of one dimensional steel/butadiene acrylnitrile rubber (NBR) periodic structure. The calculation results are in good agreement with the experimental results. Further theoretical analyses shows that the nonlinear changing of elastic constants with frequency of viscoelastic rubber can remarkably increase the width of first band gap, and at the same time hold the starting frequency of it. For the two cases, the width of first band gap increased by 36.4% (for the 3 mm steel/10 mm NBR periodic structure) and 34.0% (for the 7 mm steel/10 mm NBR periodic structure) respectively.

Key words: Plane wave expansion, Phononic crystals, Vibration band gap, Viscoelasticity