Further Dynamic-integrity-based Reliability Analysis

Abstract

Abstract Non-linear dynamical systems of different areas of engineering and technology are subject to parameters that should most of the times be realistically modelled as random variables, although they are usually considered to be deterministic. This paper addresses in a simple, almost naïve fashion, the reliability analysis of those systems, starting from a deterministic analysis, but then bringing into it the statistical properties of input variables. Although the concept of dynamical integrity has greatly contributed to establishing safe thresholds in dynamical systems, requiring that the basins of attraction should be robust, a reliability measure is still missing in that respect. In fact, supposing that the erosion curve of a dynamic integrity measure I (for instance, the integrity factor) has been obtained in terms of a system parameter A (for instance, a load amplitude, a load frequency, or still an imperfection parameter) using a deterministic approach, one can estimate the output statistical properties for I, in terms of those of the input parameter A, now considered as a random variable in its own right. Hence, once reference values for the integrity measure I ref and the system parameter A ref have been established, and assuming that increase of A beyond A ref may prove to be dangerous, the probability that I ≥ I ref, provided that A ≤ A ref, would give a sound reliability assessment. A very simple approach towards this aim is proposed and applied herewith to an archetypal model of a rigid column asymmetrically constrained by a linear spring, subject to a conservative axial compression and a small dynamical transversal load, playing the role of a random dynamical imperfection. It should be said that this work is a continuation of another one, with the same archetypal model, yet taking into account only the effect of a statical imperfection. A versatile in-house code is used to obtain the basins of attraction and the erosion curves that give support to the proposed methodology. The reliability assessment is carried out in two different scenarios, namely varying either the dynamical imperfection amplitude or its frequency. The influence of nearness to either buckling, or to external resonance or even parametric resonance can be studied according to the proposed methodology. It is simple and easy to be applied. Therefore, one hopes that it can be absorbed in engineering design practice without its traditional resistance to incorporate new trends.