Nonnormal Secondary Response Due To Yielding in a Primary Structure
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Response nonnormality is investigated for a linear secondary system which is mounted on a yielding primary structure subjected to a normally distributed ground acceleration. The nonlinearity considered in the primary structure is bilinear hysteretic (BLH) yielding. The coefficient of excess (COE), which is a normalized fourth cumulant function, is used as a measure of the nonnormality in the current study. This work is a follow up to an earlier study in which it was demonstrated that the response acceleration of the primary system can be significantly nonnormal in some situations. Linear substitute methods are used for analytically evaluating the nonnormality of secondary response. The basic concept is to use a linear model with nonnormal excitation to replace the nonlinear primary element with normal excitation, with the goal of matching the trispectrum for the acceleration of these two systems. A two filters model (with a more narrowband fourth cumulant filter) gives good approximations for the COE values of secondary response in most cases including both cascade and noncascade analysis. The probability of failure from either first-passage or fatigue is investigated for secondary response affected by nonnormality. It is shown that the nonnormality effect generally is more significant for first-passage failure than for fatigue failure based on the cases in this study, and both failure modes can be significantly affected by the nonnormality in some situations.