非线性模型修正的等效线性化方法

Nonlinear model updating strategy based on equivalent linearization method

利用模型分析和试验分别得到的结构特征量建立优化目标函数是结构模型修正的关键。但非线性结构的特征量不如线性结构的丰富,而且不易通过常规试验技术提取;特别是在随机振动工况下,非线性结构的动力特性将更加复杂,对其进行理论研究或试验分析都存在困难,因此也不易实现模型修正。等效线性化是进行非线性系统随机振动分析的有力手段;同时,等效线性系统的唯一性使其有望成为非线性系统的重要特征量之一。利用相对坐标提出一种非线性系统等效线性化的数值计算方法,并利用所得到的等效线性系统作为非线性系统特征量建立模型修正目标函数,从而提出了一种基于等效线性化数值计算方法的非线性模型修正策略。结果表明:该策略能够准确进行非线性系统的等效线性化数值计算,并有效提升非线性模型的精确度,实现非线性模型修正。

The optimization objective function established by structural eigenvalues obtained from numerical model and dynamic experiment is crucial for model updating.However,the eigenvalues of nonlinear structures are not as rich as those of linear structures,and they are not easy to be extracted by conventional test technology.Especially in the case of random vibration,the dynamic characteristics of nonlinear structures will be more complex,and it is more difficult to carry out theoretical or experimental analysis,and therefore it is hard to achieve model updating.Equivalent linearization is a powerful method for random vibration analysis of nonlinear systems.At the same time,the uniqueness of the equivalent linear system makes it possible to become one of the important eigenvalues of the nonlinear systems.Firstly,a numerical calculation method of equivalent linearization for nonlinear systems was proposed by using relative coordinates,and the obtained equivalent linear system was used as the eigenvalue of nonlinear systems to establish the model updating objective function,thus a nonlinear model updating strategy based on equivalent linearised numerical methods is proposed.Calculation results show that the proposed strategy can accurately perform the equivalent linearised numerical calculations of the nonlinear system,effectively improve the accuracy of the nonlinear model,and realize the correction of the nonlinear model.