Random earthquake response analysis for an energy dissipation structure adding viscous dampers

The dynamic responses of a multi-degree of freedom seismic reduction structure with a viscous damped brace under a random earthquake motion model were analyzed. The earthquake induced ground motion was assumed to be a zero mean stationary filtered Gaussian white noise process with a Kanai-Tajimi power spectrum. The equivalent linear viscous damping coefficient was considered as the damper parameter for simplicity of analysis and the dynamic equation of the structure with energy dissipation device was established. According to the special situation that the modal equations were coupled through the viscous damping term built into the structure, the motion equation of the structure with viscous dampers under the random earthquake motion model was represented by the state equation. In the state space, the complex mode method and random vibration theory were used to establish the calculation method and deduce the stochastic response analytic solutions of the structure with viscous dampers and energy dissipation device in time domain, respectively. Finally, the proposed method was applied to a frame structure adding viscous fluid dampers. By introducing the conception of state space, the vibration equation of the structure with viscous dampers could be uncoupled and the analytic solution of the variance response of the structure with viscous dampers could be obtained conveniently in time domain. This practical method could provide a basis for reliability assessment and reliability-based optimization of vibration energy dissipation structures with viscous dampers.