基于复振型分解的多自由度非线性体系动力可靠性研究

提出了基于复模态理论的多自由度非线性体系动力可靠性分析方法。该方法首先采用等效线性化的方法处理体系的非线性问题,然后采用复模态分析处理非经典的等效线性阻尼矩阵,将具有非经典阻尼的等效多自由度线性体系按复振型分解,将多自由度体系的随机反应分解为一系列一阶体系的复模态反应,从而求得体系的随机反应,最后进行体系的动力可靠度计算。通过算例验证,表明该方法概念明确、思路清晰,为一般多自由度非线性体系提供了一个普遍适用的动力可靠性分析方法。

Study on multi-degree-of-freedom nonlinear system dynamic reliability based on complex mode decomposition

Dynamic reliability analysis method for multi-degree of freedom nonlinear system based on complex modal theory is proposed.The method uses equivalent linear method to deal with the nonlinear problems of the system firstly.Then complex modal analysis is used to deal with the non-classical equivalent linear damping matrix,the equivalent MDOF linear system,the damping of which is non-classical,is uncoupled according to the complex mode,that is,the random responses of MDOF system are uncoupled to a series of first-order system of complex modal responses,thus the random responses of the system are obtained,and finally the system dynamic reliability calculation can be done.By example checking,the method is a universal dynamic reliability analysis method for general multi-degree-of-freedom nonlinear system with clear concept and clear thinking.