The Effect of Semi-active Control on Nonlinear Response of Structures through Incremental Dynamic Analysis

It this paper, incremental dynamic analysis (IDA) of the controlled structures is presented. Nonlinear dynamic analyses for controlled structures are performed through Force Analogy Method (FAM) and State-space. IDA curves are demonstrated for un-controlled structures, under optimal control and under semi-active control. Therefore, the influence of control system for structures and changes in its behavior could be observed. Introductions for IDA, structural control, Semi-active Hydraulic Damper (SHD) and Force Analogy Method (FAM) are explained in the article. Full Static Condensation Model (FSCM) is introduced as a recent method that could consider non-linear behavior (through FAM and State-Space), static condensation and full Rayleigh damping matrix. In this article, FSCM is extended for the structures which are protected by optimal or semi-active control system. Therefore nonlinear behavior of controlled structures was considered. Numerical examples for a 5-story frame under scaled earthquakes were presented. The structure, for both controlled and un-controlled conditions, was modeled by the way that it could consider non-linear behavior. Control algorithms that have been used in the program were optimal control and SHD semi-active control. Programming was performed in MATLAB and IDA curves for no-control, optimal control and SHD control (with different arrangements of SHD control tools) are calculated and illustrated. At the end of the numerical section, some results and interpretations were extracted from IDA curves of controlled and un-controlled. They are explained in details and could give better understanding for dynamic behavior of the structures.