Construction of orthogonal projector for the damage identification by measured substructural flexibility

Shun Weng, Hong Ping Zhu, Peng Hui Li, Yong Xia, Ling Ye

Research output: Journal article publicationJournal articleAcademic researchpeer-review

8 Citations (Scopus)


In the substructuring methods, the global structure is divided into free–free substructures. The independent substructures move freely, and their stiffness matrix is singular and rank-deficient. The flexibility matrix of the free–free substructure, which is associated with the inverse of the stiffness matrix, is not easy to be determined. This study expands on the previous research of the substructuring methods by taking a deeper look at the analysis of a free–free substructure. An orthogonal projector is formulated to add/remove the rigid body components from the generalized stiffness and flexibility matrices of a free–free substructure, and thus make the substructural flexibility useful to model updating or damage identification. The orthogonal projector is derived both for the full and partial measured flexibility, and it can remove all rigid body components regardless its participation factor. The accuracy of the proposed method in extraction of the free–free flexibility and in damage identification is verified by an experimental beam. The properties addressed in this paper are not limited to be used for the analysis of a free–free substructure in many substructuring methods, and they are promising to be generalized to a range of analysis relevant to a free–free structure.
Original languageEnglish
Pages (from-to)441-455
Number of pages15
JournalMeasurement: Journal of the International Measurement Confederation
Publication statusPublished - 1 Jun 2016


  • Damage identification
  • Flexibility matrix
  • Orthogonal projector
  • Rigid body modes
  • Stiffness matrix
  • Substructuring method

ASJC Scopus subject areas

  • Instrumentation
  • Electrical and Electronic Engineering

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