动力响应问题的摄动Riccati传递矩阵方法

基于Riccati传递矩阵法,给出了一维不确定参数结构系统动力学响应问题的二阶摄动计算方法。该方法在用于一维结构系统动力响应问题的摄动分析时,不需要按振型展开,避免了基于有限元的矩阵摄动方法所带来的模态截断误差问题,提高了分析结果的精度。以多跨转子——轴承系统为模型,导出了动力响应问题摄动R iccati传递矩阵法的具体计算公式,并编制了相应的计算分析程序。算例对弹性支承的等截面梁的动力响应问题进行了摄动分析,摄动计算结果和精确计算结果吻合良好。

Perturbation Riccati Transfer Matrix Method for Dynamic Response Problems

We use the Riccati transfer matrix method to present a second-order perturbation calculation method for the dynamic response problem of a one-dimensional structural system with parameter uncertainties. The perturbation calculation method avoids the modal truncation errors caused by the FEM-based matrix perturbation method, thus enhancing the accuracy of perturbation analysis results. Setting the rotor-bearing system with multiple spans as a model, we derive the calculation formulas of the perturbation Riccati transfer matrix method for dynamic response problems and develop its computational program. The method is applied to the perturbation analysis of the dynamic response from a beam with spring supports at both ends, and the perturbation calculation results agree well with the accurate calculation results.