多自由度柔性结构非线性随机振动响应分析方法

随机等效线性化方法是多自由度结构非线性随机振动分析的有效方法,然而柔性结构隐式的系统方程限制了该方法的应用.本文首先提出了把多自由度柔性结构隐式系统方程显式化的等效非线性系统建立方法,该方法结合模态分析,将系统几何非线性作用等效为模态坐标的高次多项式组合,把多自由度物理系统转化为容易求解的模态系统;在此基础上运用随机等效线性化技术建立柔性结构非线性随机振动响应分析方法.该方法通过引入虚拟激励原理,大幅提高了计算效率,使对多自由柔性结构的非线性随机振动响应分析成为可能.通过算例分析,本文分析结果和精确解与数值模拟解的比较结果表明,本文方法具有较好的计算精度和较高的计算效率,能够应用于实际柔性工程结构的随机振动响应分析.

Nonlinear random vibration of multiple-degree-of-freedom flexible structures

Stochastic equivalent linearization method has gained wide popularity because of its versatility in application to multi-degree-of-freedom nonlinear systems. It's restricted in the random vibration analysis of flexible structures because of the implicit nonlinearity of the system. This paper presents a new method for the equivalent nonlinear system of flexible structures. Using this method,the implicit geometrically nonlinear system can be represented as an explicit equivalent nonlinear system. According to the modal analysis method,the geometrically nonlinear force is replaced by a high-order moment of modal coordinate. The multiple-degree-of-freedom (MDOF) physical system is translated into a modal system,which could be solved easily. Based on the equivalent nonlinear system,the nonlinear random vibration method is presented by using stochastic equivalent linearization technology. By using the pseudoexcitation method,the efficiency of the nonlinear random vibration method is increased obviously. The rapid calculation makes it possible to analyse the nonlinear random vibration of multiple-degree-of-free-dom flexible structure. The validation shows that the method has reasonable precision and high efficiency and it could be used in the random vibration analysis of practical flexible structures.