Instantaneous earthquake input energy and sensitivity in base-isolated building

The input energy and energy input rate to a base-isolated (BI) building during an earthquake are considered and formulated in the frequency domain. The frequency-domain approach for computation of input energy and energy input rate has different remarkable advantages compared with the conventional time-domain approach. It is demonstrated that the input energy can be of a compact form via the frequency integration of the product between the input component (squared Fourier amplitude spectrum of acceleration) and the structural model component (so-called energy transfer function). Furthermore, the energy input rate can also be of a similar form via the frequency integration of the product between the instantaneous power spectrum and the energy transfer function. With the help of this compact form, it is shown that the formulation in the frequency domain is essential for deriving arbitrary-order closed-form sensitivities of the input energy and energy input rate with respect to uncertain stiffness and damping coefficients in the BI storey. The closed-form sensitivity expressions provide us with information on the most unfavourable variation of the uncertain parameters that leads to the maximum input energy and input rate.