Reliability of controlled linear systems under Gaussian and non-Gaussian loads

Civil and mechanical engineering systems are often subjected to vibrations which could alter their behaviour or even lead to their damage or failure. Generated either by man-made processes, such as traffic or equipment, or by natural processes, such as seismic or ocean waves, vibrations may be represented by stochastic processes defined over certain ranges of frequencies. Vibration-control systems have been developed to reduce the undesired response of systems subjected to random vibrations. The aim of the current paper is to compare comprehensively the performance of three popular passive vibration-suppression devices installed in linear single-degree-of-freedom (SDOF) systems subjected to Gaussian and non-Gaussian random vibrations with general frequency content, characterised by a power-spectral density function. The vibration-control systems analysed in this study are the viscous dampers (VD), the tuned-mass dampers (TMD) and the tuned-inerter dampers (TID), and their performance is assessed in terms of reliability metrics, such as the probability of failure and the first passage time. The twofold goal of this study is reached through (1) the development of explicit analytical relations of the controlled-systems’ responses to the Gaussian input; and (2) Monte Carlo simulation estimates of the reliability metrics for the systems subjected to the non-Gaussian loads.