Nonlinear Stochastic Response and Reliability of Secondary Systems

Abstract

The response and reliability of a linear secondary system attached to a multi‐degree‐of‐freedom yielding primary structure under white‐noise or filtered white‐noise excitations are studied by using equivalent linearization and digital simulation. It is shown that the effect of the primary‐structure yielding on response and reliability of the secondary system mainly depends on the ratio of the secondary‐system natural frequency to the natural frequencies of the primary structure and on the excitation spectral density shape in the range of natural frequencies of the primary structure. Under white‐noise excitation, amplification of the secondary system response results due both to tuning of the secondary system with one of the modes of the postyield primary structure and to an increase in excitation spectral density values at natural frequencies of the postyield primary structure. High‐frequency amplification is possible in this case. It is also shown that amplification of the secondary system response can be alleviated by increasing the damping ratio of the secondary system and by positioning the secondary system at higher levels of the primary structure.