Cubic nonlinear structural control with emphasis on non-structural performance

Most strategies in the structural control literature are aimed at improving performance of the primary structural system, but may have limited or even adverse effect on nonstructural components during strong seismic events. In this research, we emphasize nonstructural performance using a controller with cubic nonlinearities. The controller is optimized based on the frequency response functions of a SDOF nonlinear oscillator derived from our general method for a generic weakly nonlinear system. This method has its root in the Krylov- Bogoliubov asymptotical method. A benchmark eight-story base-isolated building recently proposed by the ASCE structural control committee is studied as a demonstration. We also compare the performance of the proposed cubic control system with that of a LQG-based semiactive control system and a passive energy dissipation system. It is shown from the simulation results that in most benchmark test cases, the cubic control system produces better nonstructural performance while maintaining good response characteristics of the primary structural system, which verifies our theoretical derivation. Another feature of this research is that it also discusses the fundamental qualitative concepts such as stability, together with the quantitative optimal determination of the controller. The qualitative theory is of utmost importance in practical applications. Thus, while this research presents a comprehensive analysis and design of the cubic control system at a basic level, more advanced aspects are also noted.