Theoretical and experimental structural damage diagnosis method using natural frequencies through an improved sensitivity equation

In this study, a frequency-based technique is presented to detect any number of localized damages which induce stiffness reduction in a structure. The sensitivity of natural frequencies is characterized as a second order element level function of the stiffness reduction. To achieve accurate results, change in the mode shapes of the structure are expressed as a linear combination of the intact structure mode shapes and are considered to develop sensitivity equations. The overall formulation yields an indeterminate set of equations. An optimization criterion is used to solve these equations to obtain the change of the structural parameters. The method was applied to a truss using numerically simulated data and it was verified using experimentally measured data of a steel cantilever beam and a one-story one-bay frame. Results show the efficiency of the proposed method and the importance of including the changes of the mode shapes through a frequency-based damage detection algorithm and also approve that the method is able to detect damage without an exact model of the undamaged structure.