Research on Optimal Placement of Actuators of High-Rise Buildings Considering the Influence of Seismic Excitation on Structural Modes

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).

Keywords

• Clough–Penzien spectrum model
• Luenberger observable canonical form
• controllability gramian matrix
• PBH system controllability index
• modal disturbance degree
• modal controllability degree