Ph.D Student | Daniel Yael |
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Subject | Performance-Based Retrofitting of Structures under Dynamic Loadings Using Passive Control |

Department | Department of Civil and Environmental Engineering |

Supervisors | Professor Oren Lavan |

Professor Robert Levy | |

Full Thesis text |

This research thesis presents a unified approach to solving problems of optimally allocating and sizing passive damping devices in existing structures undergoing various dynamic loadings. A general performance-based methodology for solving such problems, which is suitable to problems of a certain nature, is presented. The methodology is based on a simple analysis/redesign-type algorithm which converges to a fully-stressed design (i.e. a damper is added only to locations where the performance measure equals the allowable) in two stages. First an analysis of the structure under the given dynamic loadings is preformed and the response measures are evaluated. Based on those, the dampers' parameters are then redesigned using a recurrence relation. The advantage of using such an analysis/redesign algorithm is that the approach is general, efficient and practical for use on the one hand, yet is cost-efficient on the other. The analysis/redesign procedure relies on analysis tools only and is generally very fast converging. Although not formally proven to be optimal, in previous problems solved using a similar procedure, as well as in some problems dealt with herein, the solution obtained by the analysis/redesign procedure was compared to a solution obtained using formal optimization with good agreement. It is assumed, therefore, that in general the solutions obtained by the analysis/redesign procedure are optimal, or at least close to that. Methods for verifying the optimality of the solution obtained using this procedure are also presented.

To demonstrate the use of this approach, three different distinct dynamic control problems are presented, utilizing two different types of damping devices. The first problem regards the control of frame structures undergoing severe ground motions using friction/hysteretic dampers, the second problem relates to control of pedestrian bridges using multiple tuned-mass dampers and the third problem addresses the seismic control of structures using multiple tuned-mass dampers for both deterministic and stochastic representations of ground motions. For the first problem, optimality of the solution obtained by the proposed methodology is confirmed. This is done by comparing the solution obtained using the analysis/redesign scheme to that obtained by solving the optimization problem using formal gradient-based optimization tools. For use in the formal optimization process, the gradients of the objective function and constraints of this problem were analytically derived. For the second problem, optimality of the solution obtained was also shown, this time utilizing symmetry conditions to obtain a graphic solution to the optimization problem.