Response Analysis Of Multi-Degree-of-Freedom Nonlinear Stochastic Hysteretic System

The research on nonlinear vibration is an attracting and important study field in the research of mechanics recently. Almost all systems exhibit nonlinear in some degree. It is not effective for many actual engineer questions if solved only from the point of linear and determination views. Based on two reasons ,we adopt nonlinear models: first ,furthermore exact quantitative analysis is expected to find for the certain problems ;second ,linear models can not even make with reasonable explains and right qualitative analysis for the essence nonlinear phenomena ,So it is very necessary to study the nonlinear random vibration systems. Hysteretic system is one of the most typical nonlinear systems. Many engineer structural systems under dynamic loading usually exhibit hysteretic behavior, especially when the response becomes inelastic. A hysteretic loop produces between hysteretic restoring force and displacement under periodic movement. The effect exhibits the change of stiffness and energy. Because the restoring force of a hysteretic system depends not only on the instantaneous displacement, but also on its past history, analytical modeling and solution of such a system under random excitation has been an interesting and challenging subject. The hereditary nature of the restoring force of an inelastic system indicates that the force can on longer be described by an algebraic function of the instantaneous displacement and velocity. The research on hysteretic system concentrated on three aspects: Firstly: Hysteretic restoring force models. People have developed many different hysteretic restoring force models according to different engineer structural system needs in recent years, for example: Bilinear model,Ramberg-Osgood model,Differential equation models,Bilinear and multilinear model and Biaxial interaction model,etc.But every kind of model has definite limitation。At the present time Bouc-Wen differential coefficient model is used abroad in the research on hysteretic system。Recently,dissymmetrical model is developed。Secondly: The response of hysteretic system under random excitation. According to the hysteretic restoring force models People have solved the response of such hysteretic system under random excitation. The main methods include in K-B approximation for bilinear systems, Semi empirical method for elastic-plastic systems,Equivalent linearization method for smooth systems,and Markov vector and Fokker-Plank equation method, etc. Applying above these methods,it has soved the response of single-degree-of-freedom or multi-degree-of-freedom hysteretic system under random excitation according todifferent requires .Thirdly: Hysteretic system parameter identification. Generally, we can analysis of the response of system and energy dissipation and degrading after we know the hysteretic nonlinear relation of displacement and load of system. A simple technique based on a least square error minimization has been developed for the smooth hysteretic models. Other methods such as those based on an extended Kalman filter method have been applied to the smooth hysteretic restoring force successfully. To hysteretic system ,it is familiar that one model is firstly supposed basing on experience and such the parameters are recognized using vary means.Except above-mentioned measures,the methods of non-parameter recognizing are effective。The research that mentioned above solves the response of stochastic hysteretic systems under random excitation, but people do not solve the random response of nonlinear stochastic vibration system that caused by the hysteretic loop that is random itself. But the semi-continuous medium in engineer mechanism stands out especially, because of the discrete character of material, which leads to the nonlinear random vibration model of hysteretic system. A lot of engineer experiments have already proved the random discrete character that lies in hysteretic loop itself. So it is very necessary to study the random vibration of nonlinear systems that caused by hysteretic loop.I...