Abstract
On the basis of the Bouc-Wen hysteretic model, the effective numerical method for the response of nonlinear multi-degree-of-freedom (MDOF) stochastic hysteretic systems is presented using second moment method. Using this method, the mean values, variances and covariances are computed. The Monte Carlo simulation is applied to validate the method. The results obtained by the two methods are contrasted, and the solutions of the method in this paper agreed very well with the Monte Carlo simulation. It has solved the random response of nonlinear stochastic vibration systems which is caused by the stochastic hysteretic loop itself.
Highlights
Hysteretic system is one of the most typical nonlinear systems
According to the above works, it could be seen that Bouc-Wen differential coefficient model has been used abroad to formulate the hysteretic restoring force, the response of single-degree-of-freedom or multi-degree-of-freedom hysteretic system under random excitation according to different requires could be solved by the existed methods and there have been some fruits which could identify the hysteretic system parameter
On the basis of the Bouc-Wen hysteretic model, the second moment method is applied to get the effective numerical method for the response of multi-degree-of-freedom stochastic hysteretic system that is caused by uncertain hysteretic loop itself
Summary
Hysteretic system is one of the most typical nonlinear systems. Many engineering structural systems under dynamic loading usually exhibit hysteretic behavior, especially when the response becomes inelastic. The modeling and analysis for the hysteretic nonlinear system which is applied by deterministic excitation and is with the stochastic parameters have been developed in [19]. According to the above works, it could be seen that Bouc-Wen differential coefficient model has been used abroad to formulate the hysteretic restoring force, the response of single-degree-of-freedom or multi-degree-of-freedom hysteretic system under random excitation according to different requires could be solved by the existed methods and there have been some fruits which could identify the hysteretic system parameter. On the basis of the Bouc-Wen hysteretic model, the second moment method is applied to get the effective numerical method for the response of multi-degree-of-freedom stochastic hysteretic system that is caused by uncertain hysteretic loop itself. It has solved the random response of nonlinear stochastic vibration system that is caused by the stochastic hysteretic loop itself
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