No abstract

This paper attempts to show analytically that the energy-input spectra of damped SDOF systems and undamped MDOF systems excited by an earthquake motion can be predicted by smoothing the Fourier amplitude spectrum of the base acceleration. The spectral window for smoothing in the frequency domain for a damped SDOF system is identical with the probability density function of the time-variant or instantaneous vibration frequency resulting from non-linear hysteresis. The spectral window for an undamped MDOF system is identical with the set of squared participation factors associated with vibration modes. It was found that the increase in damping factor and the increase in participation of higher modes provide wider spectral windows, resulting in more flattened or unaltered energy-input spectra due to enhanced smoothing effects.