Stochastic sensitivity analysis of nonlinear primary-secondary structural systems

A response and sensitivity analysis of the mean-square response of secondary systems attached to yielding primary structures is presented. The main objective is to examine the effect of nonlinearity in the primary structural behaviour on the response characteristics and its sensitivity to secondary systems in a stochastic environment. The procedure follows equivalent linearization with partitioning in order to alleviate the dimensionality problem. Under white noise excitation, results show that yielding of the primary structure generally favours the secondary system response and its sensitivity, except in the tuning region in which amplification can take place due to the frequency shift of the yielding primary structure. With regard to the placement problem of secondary systems, while position sensitivity varies significantly in the linear case, yielding of the primary structure tends to produce a smoothing effect, leading to a more uniform sensitivity behaviour.