Statistics of cumulative damage parameters based on hysteretic energy dissipated

Abstract The statistics of hysteretic energy dissipated by nonlinear-hysteretic oscillators under random dynamic loading are discussed. It is observed that the first two moments (mean and variance) of the hysteretic energy dissipated behave in the same manner as the corresponding statistics of cumulative damage parameters based on linear damage accumulation. The paper also discusses how the hysteretic energy dissipated per loading cycle or some appropriate functions of it may be used as a measure of cumulative damage for some non-deteriorating and deteriorating structural components. Then, statistics of cumulative damage parameters based on the hysteretic energy dissipated per loading cycle are computed using random vibration analysis.