Abstract
Passive liquid dampers have been used to effectively reduce the dynamic response of civil infrastructures subjected to earthquakes or strong winds. The design of liquid dampers for structural vibration control involves the determination of the optimal parameters. This paper presents an optimal design methodology for tuned liquid column dampers (TLCDs) based on theH∞control theory. A practical structure, Dalian Xinghai Financial Business Building, is used to illustrate the feasibility of the optimal procedure. The model of structure is built by the finite element method and simplified to the lumped mass model. To facilitate the design of TLCDs, the TLCD parametric optimization problem is transferred to the feedback controller design problem. Through the bounded real lemma, an optimization problem with bilinear matrix inequality (BMI) constraints is constructed to design a static output feedbackH∞controller. Iterative linear matrix inequality method is employed and it added some value range constraints to solve the BMI problem. After the TLCD parameters are optimized, the responses of displacement and acceleration in frequency domain and time domain are compared for the structure with and without TLCD. It is validated that the TLCD with the optimized parameters can make the structure satisfy the need for safety and comfort.
Highlights
Civil structural buildings can be damaged under heavy excitation, such as earthquake
This paper employs the iterative linear matrix inequality (ILMI) method proposed by Cao et al [10] and adds the constraints (21) into this method to numerically calculate the static output feedback controller G
After the assumed Tuned liquid column damper (TLCD) is optimized, it would be divided into three same TLCDs, whose total mass ratio, frequency tuning ratio, and damping ratio are, respectively, equal to the optimized parameters
Summary
Civil structural buildings can be damaged under heavy excitation, such as earthquake. TLCD can be designed to make its dynamics be suitable for the vibration control of a building. TLCD can be set in the building as a liquid tank and used for vibration control. According to the bounded real lemma [7], designing the static H∞ controller is an optimization problem with bilinear matrix inequality (BMI) constraints. [8] produced a simple expression of the controller, in which the corresponding symmetric variable matrix in the bounded real lemma is congruent with a block diagonal matrix. Zecevicand Siljak [9] present another method to design the static output feedback controller by making some transformations between the output matrix and controller matrix.
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