AN APPROXIMATE TECHNIQUE FOR DAMAGE IDENTIFICATION IN BEAMS USING NONLINEAR REGRESSION ANALYSIS OF BENDING FREQUENCY CHANGES Elma EKINOVIC 1 , Vlatko DOLECEK 2 , Slavko DOLINSEK 3 , Nedim HODZIC 1 1 University of Zenica, 2 University of Sarajevo, BOSNIA & HERZEGOVINA 3 University of Primorska, Koper, SLOVENIA ABSTRACT: This paper addresses the problem of damage identification in beam-like structures on the base of bending frequency changes. The identification of damage location and its depth is performed by use of regression relations between changes in natural frequencies and damage parameters. Input data for establishing the regression relations are collected using numerical analysis (FEA) of the beam structure with and without damage. The damage is simulated as a narrow open notch perpendicular to the beam axis. The efficiency and limitations of the proposed technique are assessed through a series of damage scenarios. KEYWORDS : damage identification, finite element analysis, nonlinear regression 1. INTRODUCTION Identification of damages in structures and components is an important aspect of their proper operation. Failure to detect damages has various consequences, and they vary based on the application and importance of the structures and components. A number of non-destructive techniques are available now to detect faults and defects in a structure. Nevertheless, great efforts are still put towards developing new, more reliable, efficient, and less tedious detection techniques. The most common of these methods is the vibration based damage detection and identification. The basic idea behind the vibration based identification technique is that any change in the physical properties of a structure caused by the presence of a defect will directly cause some changes in the modal parameters, such as natural frequencies, damping factors, and mode shapes. These changes can be measured using the available modal testing methods. On the other hand, having sufficient data from numerical analysis enables an engineer to derive the regression relations that correlate specific shifts in one or more of the modal parameters as a function of the size and location of defects, [6]. Numerous methods have been proposed to identify damage parameters in structures. The method of using experimental modal analysis for detecting cracks appeared in the 1940s. A comprehensive survey of the available literature was given by Dimarogonas [4] and Doebling et al. [5]. These reports reviewed various technical literatures on detection and identification of structural damage using vibration based testing. Salawu [12] presented identification techniques that use only frequency information to identify damage in structures. This paper proposes a technique to identify the location and magnitude of a damage in a beam- like structure using numerical analysis and nonlinear regression. The changes that occur in the first four of its lowest bending frequencies are used for the identification of the crack parameters. 2. PROPOSED IDENTIFICATION TECHNIQUE 2.1. Formulation of the problem The fundamental idea underlying the process of crack identification is based on the fact that a change in physical parameters of the structure causes a change in its modal parameters. This fact is represented by the following matrix equation for undamped natural vibrations, Eq.(1): 0 Kq q M = + & & (1) where is the mass matrix, M K is the stiffness matrix, and and are the acceleration and displacement vectors, respectively. The eigenvalues of Eq. (1) correspond to the undamped natural frequencies of the structure. q & & q Tome VII (year 2009), Fascicule 3, (ISSN 1584 – 2673) 192