Dynamic reliability analysis of nonlinear structures using a Duffing-system-based equivalent nonlinear system method

Abstract

To improve the analysis accuracy of dynamic reliability of a nonlinear system, an equivalent nonlinear system method is presented. In this method, general nonlinear systems are converted to equivalent Duffing nonlinear systems according to the minimum mean square error criterion, whose exact analytical solution of the random steady-state responses can be determined by a FokkerPlanckKolmogorov equation. Then the exact results of stochastic responses are used to analyze structural dynamic reliability. To use the equivalent nonlinear system method to analyze structural dynamic reliability is not only convenient for calculation but highly accurate. In addition, the presented equivalent nonlinear system has a parameter ε, which controls the degree of nonlinearity. Thus, it is easy to obtain the corresponding analysis results from converting the original system to equivalent nonlinear systems with different degrees of nonlinearity by changing the value of ε. Especially, when ε is zero, the equivalent nonlinear system will degenerate to the linear system, and leading to the analysis results of the equivalent linearization method. An example shows that the analysis results of the proposed equivalent nonlinear system method are reliable, and the calculation appears to be more accurate than that of the equivalent linearization method.