Abstract
Presently, most of the common placement methods of actuators are based on the structural response and system energy to select the optimal locations. In these methods, the contribution of controllability and the energy of seismic excitations to each mode of the structure are not considered, and a large number of cases need to be calculated. To solve this problem, the Clough–Penzien spectral model is combined with the Luenberger observable normal form of the system to calculate the energy of each state. The modal disturbance degree, considering modal energy and controllability, is defined by using the controllability gramian matrix and PBH system controllability index, and the modes are divided into the main disturbance modes (MDMs) and the secondary disturbance modes (SDMs). A novel optimal placement method of actuators based on modal controllability degree is proposed, which uses MDMs as the main control modes. The optimal placement of actuators and the vibration control simulation of a 20-story building model are carried out. The results show that the vibration reduction effect of the proposed placement method is significantly better than that of the method of uniformly distributed actuators (Uniform method) and the classical placement method of actuators based on the system controllability gramian matrix (Classical method).
Highlights
IntroductionWith the progress of engineering technology and rational use of land resources, high flexibility has become the main development direction of building structures, which leads to the gradual replacement of middle- and low-rise buildings with high-rise buildings
Referring to the definition of the modal disturbance degree, we developed a modal controllability degree index, considering system controllability and input energy, and proposed an optimal placement method of actuators based on the modal controllability degree
Based on the state-space representation of the Luenberger observable canonical form which can be used to calculate the energy of each state, the evaluation index to measure the disturbance degree of seismic excitations to each mode of the structure were proposed and the structural modes were divided into main disturbance modes (MDMs) and secondary disturbance modes (SDMs)
Summary
With the progress of engineering technology and rational use of land resources, high flexibility has become the main development direction of building structures, which leads to the gradual replacement of middle- and low-rise buildings with high-rise buildings Due to their high flexibility, high-rise buildings are vulnerable to damage from seismic excitations, such as the collapse of the 22-story Pino Suarez Complex building in the Mexico City earthquake [1], the severe damage to high-rise buildings of Santiago in the Chile earthquake [2,3], and the excessive inter-story drift ratio of some high-rise buildings in Osaka and Tokyo from the Tohoku earthquake [4,5,6]. In view of the anti-seismic problem of high-rise buildings, researchers have completed a large amount of theoretical and experimental work in the field of passive, active, and semi-active control, among which active control methods have been widely used due to their good control effect and fast response [6]
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