Moving Resonance in Nonlinear Response to Fully Nonstationary Stochastic Ground Motion

A parsimonious stochastic seismic ground-motion model is used to study the effect of ground-motion nonstationarities on the response of simple linear and softening nonlinear systems. This model captures with at most nine parameters the features of the ground motion which are important for computing dynamic response, including the amplitude and frequency-content nonstationarities of the earthquake. Simple approximate expressions for the mean-square response statistics are obtained and are used to demonstrate analytically the importance of modeling the temporal nonstationarity in the frequency content of the ground motion, not only as expected for the nonlinear system, but also for linear systems. For the nonlinear systems, the phenomenon of ‘moving resonance’ is demonstrated whereby the shortening of the system frequencies, due to stiffness softening with increasing amplitudes, tracks the shift of the dominant frequencies of the ground motion, leading to a large resonant build-up in response amplitudes