The effectiveness of vibration control by connecting adjacent buildings with dampers and springs has been studied, and applied for retrofit of existing buildings and even for design of new buildings. However, the need of separate buildings limited the exploitation of the great potential and efficiency of this type of control strategy. One significant feature of the connected system is a new overall stiffness matrix that is utterly different with ordinary buildings or structures constructed by traditional methods. As a generic problem, strategies for optimal structural control may be further discussed based on model with possible arbitrary vibration characteristics. If this is advantageous, then the next step is to realize the scheme for the assumed vibration characteristics practically and economically. In this paper, two masses of a single building are connected by rocking and lever mechanism, and constructing a vibration system with variable stiffness matrix utterly deferent from traditional structure that have only a predominant first vibration mode. Based on the similarity in stiffness matrix, this new type of structure is optimal designed using formulas already developed for separate buildings linked together. It was found that the peak magnification factor could be greatly reduced for stable vibration, and a rapid damping of maximum response subjected to earthquake waves was also recognized. However, the reduction in earthquake response may not be significantly according to ground motions. As no special devises are needed for this new structure, it is expected that the arbitrary formulation of stiffness matrix be further investigated for both passive and active vibration controls.
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