Energy Stochastic Seismic Spectra for Hysteretic Structures

Seismic spectra are fundamental tools in earthquake engineering due to their intuitive conceptual framework and broad practical applicability. However, when extended to nonlinear structural analyses, such methods often require approximations that significantly compromise result accuracy. This study presents a comprehensive evaluation of the seismic response of hysteretic nonlinear systems, focusing on the energy-based aspects of the response. The Bouc–Wen model is adopted to accurately capture the hysteretic behaviour of structures subjected to intense cyclic loading. This model effectively represents the nonlinear dynamics commonly observed in structural materials under seismic excitation. The seismic input is modelled using a stochastic approach, specifically as a time-modulated, filtered, non-stationary stochastic process. This allows for a realistic simulation of seismic events, accounting for both temporal and spectral variability. The analysis involves computing the system’s response covariance and deriving the mean values of various energy components, with a particular focus on dissipated energy. By emphasizing energy dissipation, the study investigates how structural parameters and earthquake features—such as strong motion duration and Arias intensity—affect energy absorption and dissipation mechanisms. The findings aim to inform more resilient structural designs and contribute to enhanced seismic performance