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

Alin Radu,Irina F Lazar

doi:10.1007/s40435-019-00562-5

Abstract

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.

Highlights

Mitigation of unwanted vibrations represents an important research topic for many engineering disciplines
Similar to some previous studies aforementioned, this paper analyses the response of vibration-controlled linear systems subjected to Gaussian vibrations, but it compares the performances of the viscous damper (VD), tuned-mass damper (TMD) and tuned-inerter damper (TID) using explicit frequency-response relations for random vibration with general frequency contents
Analytical relations can be written for the reliability of systems subjected to Gaussian input [31,37], while for non-Gaussian problems approximate methods have been suggested [35,48], even though the only general and reliable method for calculating reliability metrics remains Monte Carlo

Summary

Introduction

Mitigation of unwanted vibrations represents an important research topic for many engineering disciplines This reduction of vibrations is commonly achieved via vibrationisolation systems, i.e. by controlling the supporting structure [1]; or via vibration-suppression systems, i.e. controlling the structure itself by means of supplemental damping [2,3] or other techniques [4,5]. This problem can be very challenging given the complexity of engineering systems and the random character of vibrations.

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Conclusion