Abstract: In order to ensure the safety of the viaduct in the state of strong vibration, it is necessary to set up a wire rope shock absorber in the viaduct to improve the frequency response characteristics of the shock absorption system. The wire shock absorber designed is mainly in the centripetal form, and the position of the wire rope through the screw is locked to reduce the deformation amplitude of the wire rope. The optimization process of the frequency response characteristics of the shock absorber under the action of excitation was analyzed. The nonlinear function of the frequency response characteristics of the damping system is reduced by using the numerical iterative method. The experiments show that the minimum peak value of frequency response amplitude is only 0.3 m when m₁=0.09 kg and m₂=0.49 kg. When c₁=0.69 N·s/m and c₂=1.49 N·s/m, the minimum peak value of frequency response amplitude was 0.23 and 0.17 m, respectively. When k₁=4.9 N/m and k₂=99.9 N/m, the minimum peak value of frequency response amplitude was 0.30 m. When z_s=0.29 N, the minimum peak value of frequency response amplitude is 0.33 m. When this is used as a parameter of mass, damping, stiffness and hysteresis, the frequency response characteristics in the vibration reduction system are the least obvious, which helps to reduce the frequency response characteristics in the vibration optimization system.