Extraction of Substructural Flexibility from Global Frequencies and Mode Shapes

A computational procedure for extracting substructure-by-substructure flexibility properties from global modal parameters is presented. The present procedure consists of two key features: an element-based direct flexibility method which uniquely determines the global flexibility without resorting to case-dependent redundancy selections; and, the projection of cinematically inadmissible modes that are contained in the iterated substructural matrices. The direct flexibility method is used as the basis of an inverse problem, whose goal is to determine substructural flexibilities given the global flexibility, geometrically-determined substructural rigid-body modes, and the local-to-global assembly operators. The resulting procedure, given accurate global flexibility, extracts the exact element-by-element substructural flexibilities for determinate structures. For indeterminate structures, the accuracy depends on the iteration tolerance limits. The procedure is illustrated using both simple and complex numerical examples, and appears to be effective for structural applications such as damage localization and finite element model reconciliation.