Optimal Gains in Mass, Stiffness and Added Damping for Seismic Upgrade of Frame Structures

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Abstract

A novel approach for the seismic retrofit of linear frame structures is presented and described. Use is made of optimal control theory to attain structural changes in stiffness coefficients, changes in mass and supplemental damping. An optimization problem that is required to satisfy constraints on maximum total story accelerations and maximum interstory is formulated. The general system interconnections paradigm is introduced as a closed-loop control system with a passive controller that consists of the structural changes and has simulated feedback on the structural response and seismic excitation. The cost function minimizes the H∞ norm of the maximum closed-loop response, single-input single-output (SISO) transfer function case. The first-order steepest descent of Apkarian and Noll [1] is introduced, utilized and enhanced to solve the optimization problem. A numerical example of a 9-story shear-type building is studied. Optimal changes in mass, stiffness and damping that are obtained, show significant improvement in the peak dynamic response. The results
clearly indicate the efficiency of the proposed methodology that possesses the capability of attaining optimal changes in all of the structure’s physical characteristics (mass, stiffness, damping) while adhering to preassigned maximum response levels.
Original languageEnglish GB
Title of host publicationProceedings of the 16th World Conference on Earthquake Engineering
StatePublished - 2017

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