Identification of Free–Free Flexibility for Model Updating and Damage Detection of Structures

Aerospace and civil structures are sometimes measured under free constraints. In many substructuring methods, the substructures are independently analyzed with free constraints as well. When a structure is free because of insufficient structural constraints, the experimental flexibility is influenced by rigid body motion. This study formulates projection matrices perpendicular to rigid body motions for removing the rigid body components of flexibility of a free–free structure. Without losing generalization, a mass-normalized projection matrix is formulated for the dynamically tested free–free flexibility, and the dynamic condensation method is used to formulate the projection matrix for the partial measurement. The proposed projection matrix not only removes all rigid body components in the measured flexibility but also constructs a dual inverse between the singular free–free stiffness and flexibility, thereby making the flexibility-based model updating feasible for free–free structures. The projection matrix is applied to a laboratory subway lining placed on the ground without constraints and to the substructuring method for substructure-based model updating. The experimental examples prove that the projection matrices are effective in the identification of free–free flexibility for model updating and damage detection.