摘要
利用POD(Proper Orthogonal Decomposition)方法结合固定界面模态综合方法,提出了一种求解局部非线性问题的降阶方法。该方法将系统分成线性、非线性子结构。对于非线性子结构,利用POD方法构造POM(Proper Or-thogonal Mode)来代替传统的线性模态,然后利用线性约束模态代替非线性约束模态。文中通过算例说明了所提方法的有效性。通过此方法,避免了求解整个系统的响应,可以将POD降阶方法推广到含局部非线性的大型有限元模型。此外还提出采用一种更新的线性约束模态来近似估算非线性约束模态的方法,并利用该方法证明了当非线性子结构为弱非线性时,用线性约束模态代替非线性约束模态的合理性。
An approach to the development of reduced order models for systems with local nonlinearities is presented. The approach is an extension of the fixed-interface component mode synthesis technique. Specifically, the case of nonlinear substructures is handled by using fixed-interface proper orthogonal mode （POM）. These normal modes are constructed for the various substructures by proper orthogonal decomposition （POD）, and are then coupled through the traditional linear constraint modes. A class of systems is used to demonstrate the concept and show the effectiveness of the proposed procedure. The proposed method is applicable to the large-scale FEM models with local nonlinearities for reducing the degree of complication in the calculation of dynamic response of a whole system. Furthermore, the updated linear constraint modes are proposed to estimate the nonlinear constraint modes. It＇s proved that it＇s more convenient to replace nonlinear constraint modes with linear constraint modes for weakly nonlinear substructures by the method.
出处
《振动工程学报》
EI
CSCD
北大核心
2008年第4期365-370,共6页
Journal of Vibration Engineering
