Statistics of Hysteretic Energy Dissipated Under Random Dynamic Loading

Abstract

An equivalent linearization technique and Monte Carlo simulation are used to investigate the statistics of the hysteretic energy dissipated by SDOF inelastic hysteretic systems under random dynamic loading. It is shown that the equivalent linearization predicts well both the standard deviation and coefficient of variation of the hysteretic energy dissipated. Under stationary conditions the standard deviation of the hysteretic energy dissipated increases with the square root of time, while its coefficient of variation decreases with the square root of time. It is also observed that the mean and coefficient of variation of the hysteretic energy dissipated depend mostly on the ductility demands of the loading, the bandwidth of the response process, and the elastic frequency of the oscillator. The first two moments of the energy dissipated by hysteresis appear to behave much in the same manner as the first two moments of cumulative damage parameters based on linear damage accumulation.