The Stiffness and Flexibility of Free-free Substructure in Modal Space
Many practical structures possess rigid bodymotion due to insufficient structural constraints, and some substructures are independently analyzed under free conditions in many substructuring methods.In the case when a structure possesses the rigid body modes, the stiffness matrix is singular and rank deficient, thus many variables associated with the inverse of the stiffness matrix is not easy to be determined in usual man ner.This study expands on the previous research on the substructuring methods by taking a deeper look at the issues in dealing with a free substructure.A general form of the well-conditioned flexibility and stiffness matrices is constructed for a free structure.Some difficulties associated with the analysis of the free substruc tures, such as the analysis of eigenequation with zero eigenvalues, the formulation of the modal flexibility,residual flexibility and some derivative variables, are solved in a simple and effective way.In addition, an orthogonal projector is formulated to remove the rigid body components from the generalized stiffness and flex ibility matrices which contain both the deformational components and rigid body components.The orthogonal projector can be used to normalize the substructural flexibility extracted from the global measurement, which are applicable in substructure-based model updating and damage identification.The properties addressed in this paper are not limited to be used for the analysis of a free substructure in many substructuring methods,and they are promising to be generalized to a range of analysis relevant to a free structure.
Shun Weng Yang Chen Hongping Zhu
School of Civil Engineering & Mechanics, Huazhong University of Science and Technology, Wuhan, China
国际会议
哈尔滨
英文
724-730
2013-07-06（万方平台首次上网日期，不代表论文的发表时间）