Nonlinear System Dynamic Reliability Analysis Using Equivalent Duffing System Method

Abstract

Equivalent linearization method is the main approach for nonlinear structural system random response analysis. But it will generate big error that using the random response results of equivalent linearization method to analyze the structural dynamic reliability. In order to improve the analysis precision of dynamic reliability of nonlinear system, an equivalent nonlinear system method is presented in this paper. In this method general nonlinear systems are converted to equivalent Duffing nonlinear system according to minimum mean square error principle, whose exact analytic solution of steady state of random responses can be worked out by Fokker Planck Kolmogorov equation (FPK equation). Then the exact results of stochastic response processes are used for the analysis of structural dynamic reliability. So it is not only convenient for calculation but also with high degree of accuracy for the results that using the equivalent nonlinear system method to analyze structural dynamic reliability. In addition, the equivalent nonlinear system adopted in this work has a parameterεwhich controls the degree of nonlinear. Thus we can obtain conveniently the analysis results of converting the original system to equivalent nonlinear systems with different degree of nonlinear by changing the value of the parameterε. In particular, when the parameter ε is equal to zero we can obtain the analysis results of equivalent linearization method. It is shown from the example analysis that the analysis results of equivalent nonlinear system method presented in this paper is reliable and the calculation accuracy is higher than equivalent linear system method apparently.