1. Beijing University of Technology Beijing key Lab of Earthquake Engineering and structural Retrofit Beijing 100124,China
2. Hubei university of arts and science, Hubei Xiangyang, 441053
The research on the optimum design theory for the dissipative structure with complex damping is necessary. The dynamic equations on the tuned mass dampers (TMD) with complex stiffness and damping are established. The method for solving the optimal frequency ratio and the optimal damping ratio is presented based on fixed point theory. The steady state responses of the TMD with complex damping subjected to harmonic excitation and stationary random excitation are analyzed, respectively. The analytic solution for the optimum damping and frequency is obtained when the displacement minimization of the main structure is set as the optimum conditions. The results show that the total vibration reduction effect of the system with complex damping is close to the effect of the system with viscous damping, and the effect is better in certain frequency range when the mass ratios are the same. The random response of the TMD with complex stiffness under the Davenport spectrum is studied, and the results show that the damping effect is less than the effect under white noise excitation. The vibration reduction effect of the system with complex damping is less than the effect of the system with viscous damping, but the difference is slight. When the TMD is applied in vibration control, complex stiffness damping is an advisable option.
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