Many vibration loadings, like wind gust and landing impact acting on aerospace structures, are random and nonstationary. Analysis and designing of structures in such condition is often concerned with structure's extreme response. For most practical purposes the extreme response under random conditions is best quantified by the so-called "quantile" or 'Tractile" level, which is the response level having given probability of not being exceeded during the random loading event. In dynamic analysis, most structures are usually modeled as multi-degree-of-freedom (MDOF) systems. The extreme response of a MDOF system is most conveniently determined as a combination of the extreme modal responses of the individual modal oscillators. Although a number of studies have dealt with the extreme response of single-degree-of-freedom (SDOF) and MDOF systems under stationary conditions, very little is known about how the modal combination methods compare with the more accurate random vibration methods in quantifying the extreme response of a MDOF system under nonstationary conditions.
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