Keywords: earthquake input energy, frequency-domain analysis, time-domain analysis, residue theorem, energy transfer function, connected buildings, passive structural control, bound analysis.

Stable characteristics of earthquake input energy to elastic structures with and without passive dampers are examined by both time-domain and frequency-domain methods. Both methods support the validity of evaluating the earthquake input energy of each. It is shown that both methods have different advantages and complement each other. The frequency-domain method is characterized by the energy transfer function and its equi-area property can be derived by the residue theorem only in a simple model. It is demonstrated that this property in more general structural models can be derived by the time-domain method for an idealized model of input motions with a constant Fourier amplitude spectrum. This idea is applied to two building structures connected by viscous or viscoelastic dampers. It is concluded that the total input energy by actual ground motions to the overall system including both buildings and connecting dampers is approximately constant regardless of the quantity of connecting dampers. This property leads to an advantageous feature that, if the energy consumption in the connecting dampers increases, the input energies to the buildings can be reduced effectively. Some additional features of the frequency-domain method are discussed in detail.

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