非线性体系动力可靠性分析的等效Duffing体系法

摘要

Equivalent linear system method is the main method of nonlinear structural system random response analysis.While it would generate big error when the results of equivalent linear system method are used to analyze the structural dynamic reliability.Through minimum mean square error principle,general nonlinear system was converted to equivalent Duffing nonlinear system,based on which the structural dynamic reliability was analyzed.The accurate steady state analytic solution of Duffing nonlinear system can be worked out by FPK equation,so it is not only convenient but also accurate to analyze structural dynamic reliability by using the equivalent nonlinear system method.It is also shown that the analysis results of equivalent nonlinear system method presented here is reliable and the calculation accuracy is higher than equivalent linear system method apparently through the example analysis.%等效线性化法是非线性结构体系的随机反应分析最常用的方法,但使用等效线性化法给出的反应结果进行结构动力可靠性分析会带来很大的误差.将一般非线性体系通过均方最小误差原则等效为Duffing非线性体系来进行结构动力可靠性分析.Duffing非线性体系可以通过FPK方程求得其稳态精确解析解,所以使用该等效非线性法进行结构动力可靠性分析不仅计算上方便可行而且精度较高.算例分析表明了等效非线性法分析结果可靠,且比等效线性化法的计算精度有明显提高.