Non-random Process Model And Non-random Vibration Analysis

Engineering structures are usually subject to dynamic and uncertain external loads or excitations, which makes the responses also time-variant and uncertain, e.g. the airplane's flutter induced by atmosphere turbulence, the high-rise buildings'vibration induced by wind loads, etc. Traditionally, the stochastic process model is the principal mathematical means to deal with the time-variant uncertainty and based on the stochastic process theory, a set of methods for solving structural responses under stochastic dynamic loads have been proposed to constitute the random vibration theory and successfully applied to practical engineering problems. In their treatments, a great amount of information is required to construct precise probability distributions for time-variant uncertain external loads, which, however, is not always available or sometimes very costly for practical problems. Thus the stochastic process model and random vibration methods may be invalid in practical engineering problems. Therefore, it is of great engineering significance to develop new mathematical models for time-variant uncertainty with limited information and corresponding methods for analyzing structural responses, which are exactly the main research contents of this thesis. The main work is as follow:(1) A non-random vibration analysis method is proposed which calculates the dynamic response bounds of vibrational systems under time-variant uncertain excitations. The non-probabilistic convex model process, rather than traditional stochastic process, is used to describe uncertain dynamic excitations because the former needs only the bound information instead of precise probability distribution at any time point and therefore dependence on large sample size is weakened effectively. Based on the convex model process, non-random vibration analysis algorithms are formulated to obtain dynamic response bounds of SDOF system and MDOF system under time-variant uncertain excitations, respectively.(2) An interval process model for time-varying or dynamic uncertainty analysis when information of the uncertain parameter is inadequate is proposed. By using the interval process model to describe a time-varying uncertain parameter, only its upper and lower bounds are required at each time point. A correlation function is defined for quantification of correlation between the uncertain-but-bounded variables at different times, and a matrix-decomposition-based method is presented to transform the original dependent interval process into an independent one for convenience of subsequent uncertainty analysis. More importantly, based on the interval process model, a non-random vibration method is proposed for response analysis of structures subjected to time-varying external excitations or loads. The dynamic structural responses thus can be derived in the form of upper and lower bounds, providing an important guidance for practical safety analysis and reliability design of structures.(3) A Monte Carlo method for non-random vibration analysis is presented, which could be used for obtaining structural dynamic response intervals under uncertain excitations or loads. In non-random vibration analysis, time-variant interval variables rather than stochastic process model is used for describing uncertain dynamic excitations or loads, thus avoiding the dependency on high experimental samples. The simulation method for interval process is proposed, the sample functions generated could not only satisfy the condition of lying in the prescribed intervals, but also meet the requirements of correlation functions. Corresponding Monte Carlo method for non-random vibration analysis is presented to solve the response intervals of the vibration systems under uncertain dynamic excitations.