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The paper presents the estimation of the exact exceedance prob ability (EEP) of stationary responses of some white noise-randomly excited nonlinear systems whose exact probability density function can be known. | Vietnam Journal of Mechanics, NCST of Vietnam Vol. 22, 2000, No 4 (212 - 224) ANALYSIS OF EXCEEDANCE PROBABILITY OF DISPLACEMENT RESPONSE OF RANDOMLY NONLINEAR STRUCTURES Luu XUAN HUNG Institute of Mechanics, NCST of Vietnam SUMMARY. The paper presents the estimation of the exact exceedance p r ob abilit y (EEP) of stationary responses of some white noise-randomly excited nonlinear system s whose exact probability density function can be known. Consequently, the approximate exceedance probabilities (AEPs) are evaluated based on the analysis of equivalent linearized systems using the traditional Caughey method and the extension technique of LOMSEC. Comparisons of the AEPs versus the EEP are demonstrated. The obtained results indicate important characters of the exceedance probability (EP) as well as the influence of nonlinearity over EP. The evaluation of the applied possibility of the proposed linearization techniques for estimating AEPs are made . 1. Introduction One of the most concerned problems in the design process of types of structures, is the estimation of the extreme demands on the structure during a specified period of time. This is the same meaning with th.e estimation of exceedance probability of the extreme responses during the period of time. In general, this is a very difficult problem and usually, only indicative answers can be obtained in practice. However, in the context of civil engineering, structures subjected to environmental loads such as wind and ocean waves, a remarkable developments over the last two decades in modelling both the structure, the loading process and the interaction between them has been made. The framework usually adopted for the estimation of extreme responses of civil engineering structures for the purpose of design, is that of modelling the loading processes on the structure as stochastic processes. In cases where the dynamic behaviour of the structure can be modelled by linear equations of motion, the response .
