Closed-form equations for coupling linear structures using stiffness and damping elements

Larger and more flexible structures are being constructed. As a result, there is an increasing need for more effective, efficient, and innovative displacement control strategies. One such method is the idea of connecting adjacent structures. This control method has the merit of generating sufficient control forces under low frequencies, a property that is necessary for minimizing the displacement response of high-rise structures. In the present work, closed-form equations are derived for solving the vibration control problem of connecting two adjacent structures. In this design method, the maximum absolute displacement transmissibility of each structure is reduced. The closed-form solution is derived for a passive control method, where the structures are coupled via stiffness and damping elements connected in parallel. The presence of the stiffness element allows for the simultaneous tuning of both structures. The method is demonstrated for passive control of adjacent connected buildings subject to the El Centro ground motion. It is shown that the passive connection method is effective in reducing the response of both structures compared with the uncontrolled (unconnected) case. Copyright (C) 2011 John Wiley & Sons, Ltd.