A New Method for Estimating the Input-Energy of MDOF Structures

Input-energy is the amount of energy that is imposed by an earthquake on a structure and its correlation with structural damage has been studied and demonstrated by many researchers. Since studies concerning seismic energy in multi-degree-of-freedom systems are relatively limited compared with single-degree-of-freedom, in this paper, firstly a theoretical exact method is discussed to calculate the input-energy of the multi-degree-of-freedom elastic oscillators. It is proved that unlike the general rule in mechanics, the superposition theorem is valid for input-energy in conventional modal analysis. To estimate the input-energy, an approach based on PHSA to predict the Fourier amplitude spectrum, is proposed. The results indicate that the modal mass ratio is not the only decisive parameter in input-energy. Modal input-energy decomposition also confirms the possibility of greater input-energy of higher modes in comparison with fundamental ones or the ones with the higher mass participation ratio, especially for tall buildings located in the near-field seismic zones.