大型动力系统的降维:基于模态截断的非线性Galerkin方法

DIMENSIONAL REDUCTION OF LARGE DYNAMICAL SYSTEMS:AN NONLINEAR GALERKIN METHOD BASED ON MODEL TRUNCTION

为了有效地求解大型动力系统,现已提出了各种降维方法。根据非线性Galerkin方法的求解思路,我们将大型动力系统分解成三个子系统,即"慢子系统"、"适速子系统"和"快子系统"。在此基础上提出了改进的非线性Galerkin方法,即:在数值积分过程中将适速子系统的贡献导入慢子系统。然后,以一个含有立方非线性的5自由度强迫振动系统为例阐明了新方法的有效性。

In order to solve the large dynamical system effectively, various model reduction methods have been proposed. By analogy with the nonlinear Galerkin methods, a large dynamical system was split into a ＇slowly＇subsystem, a inoderately＇ subsystem, and a ＇quickly＇ subsystem. Accordingly, an improved nonlinear Galerkin method was developed by slaving the contribution of the moderate subsystem to the slow subsystem during numerical integration. Then, a typical 5 - degree - of - freedom system with cubically nonlinear stiffness was given to show the accuracy of the new method.