Optimal cubic nonlinear damping for seismic inter-story vibration isolation under critical double and multiple impulse inputs

Power-law nonlinear damping has been shown to be able to reduce the seismic responses of building structures over a broad range of frequencies.Many studies have been reported on the design of additional power law damping for the purpose of inter-story vibration isolation.The double and multiple impulse inputs were proposed to represent the near-fault and harmonic ground motions, respectively to facilitate a straightforward evaluation of the critical and resonant responses of elastic-plastic building systems to earthquake ground motions.In this study, a three-degree-of-freedom (3-dof) building system with a cubic nonlinear damper fitted on the second floor is considered.The nonlinear critical responses of this system to double and multiple impulse inputs with different amplitude levels are evaluated for the optimal design of the coefficient of the additional cubic damping.The optimal design is conducted based on the concept of Output Frequency Response Function (OFRF), which was derived by the frequency domain analysis of nonlinear systems and, in this study, allows the building response to the critical input to be represented as an explicit function of the damping coefficient to be designed.The objectives are to reduce the inter-story drift of each floor, the acceleration of the top floor, as well as the total vibration energy in critical cases of earthquake ground motions.The critical double and multiple impulse inputs have been defined as the inputs that can maximize the energy input into the system with their critical timing proven to be the timing when the sum of the inertial force of each floor becomes zero.The effectiveness of the optimally designed cubic damping is demonstrated using both recorded and simulated earthquake ground motions.