Earthquake input energy to tall and base-isolated buildings in time and frequency dual domains

Earthquake input energies to tall and base-isolated buildings are examined by both time-domain and frequency-domain methods. Both methods support the validity of evaluating the earthquake input energy each other. It is shown that both methods have different advantages and can compensate for each other. While the time-domain method has a long history and is applicable to nonlinear models as well, the frequency-domain method is characterized by the energy transfer function and its equi-area property plays an important role in the discussion of the stability of earthquake input energy. This equi-area property can be derived by the residue theorem only in a simple model. It is also demonstrated that this equi-area property in multi-degree-of-freedom 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 tall and base-isolated buildings. The equi-area property of the energy transfer function provides a stable characteristic on the input energy as far as the total mass of the buildings is constant.