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Three-component pillared phononic crystal plates (PPCPs) usually contain viscoelastic materials. The influence of viscoelasticity on the band structures cannot be ignored. Based on the finite element method (FEM) and the standard linear solid model, this paper proposes a method to obtain the band structures of three-component PPCP containing viscoelastic rubber. The influence of the rubber storage modulus shifting along with frequency on the vibration band gaps is investigated, and the band structures of loss factor under different relaxation time are obtained.