Identification of the stiffness distribution in statically indeterminate beams

An identification procedure is presented for the stiffness distribution in statically indeterminate structures. The proposed procedure analogous to direct calculation of the dynamic stiffness, the inverse-problem algorithm used in it is based on a finite element (FE) model of the damaged structure with unknown stiffness distribution and on a subset of measured vibration frequencies and vibration modes. The bending stiffness is updated for each element in the FE-model by an iterative procedure. In order to improve its practicability, the effect of random measurement noise is taken into consideration. A numerical study of statically indeterminate beams shows that it is able to locate both localized and multiple damage and determine its severity with a high level of reliability.