First‐Passage Time of Secondary System Mounted on Yielding Structure

Abstract

The probability of first‐passage failure affected by nonnormality (or non‐Gaussianity) is investigated through approaches that are more accurate than the commonly used analytical methods. The index used to measure the degree of nonnormality of a random process is the coefficient of excess, which is a normalized fourth‐cumulant function. The techniques are illustrated by consideration of the response nonnormality of a linear secondary system, which is mounted on a nonlinear primary structure subjected to a normally distributed ground acceleration. The nonlinearity considered in the primary structure is bilinear hysteretic yielding. It is shown that first‐passage failure can be significantly affected by the nonnormality in some situations. It is also found that the interaction force of the primary‐secondary system can significantly reduce the nonnormality of secondary response, especially when the frequency of the secondary system is tuned to that of the primary system.