In order to deal with the viscoelasticity of constituents in phononic crystals, an algorithm based on the finite-difference-time-domain method and the numerical approximation of fractional derivative are proposed. It is validated with transfer matrix method which takes the viscosity into account by complex modulus with frequency dependence. Although the viscoelasticity of host material does not influence the frequency position of gaps, a wide transmission gap is found even for very weak viscosity, which gives new idea to design phononic crystals with wide transmission gaps.
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