Earthquake input energy to two buildings connected by viscous dampers

A frequency-domain method is developed for evaluating the earthquake input energy to two building structures connected by viscous dampers. It is shown that the earthquake input energies to respective building structures and added viscous connecting dampers can be defined as works done by the boundary forces between the subsystems on their corresponding displacements. Fourier and inverse Fourier transformations enable one to transform the earthquake input energy in time domain to that in frequency domain. The earthquake input energy in frequency domain has an advantage that, while the input energy cannot be decomposed into the term for the structural parameters and that for the parameters of input ground motions in the conventional time-domain approach, it is possible in the proposed frequency-domain approach. It is demonstrated that the proposed energy transfer function is very useful for clearer understanding of dependence of energy consumption ratios in respective buildings and connecting viscous dampers on their properties. It is concluded that the total input energy to the overall system including both buildings and connecting viscous dampers is approximately constant regardless of the quantity and location of connecting viscous dampers. This property leads to an advantageous feature that, if the energy consumption in the connecting viscous dampers increases, the input energies to the buildings can be reduced drastically.