The basic idea of the proposed vibration-based damage detection method is that a damage as a combination of different failure modes in the form of loss of local stiffness in the structure alters its dynamic characteristics, i.e., the modal frequencies, mode shapes, and modal damping values. A great variety of methods have been proposed for damage detection by using dynamic structure parameters; however, most of them require modal data of the healthy state of structure as a reference. In this paper a vibration-based damage detection method which uses the mode shape information determined from only the damaged state of the structure is proposed. Effectiveness and robustness of the proposed method is demonstrated by two composite beams subjected to different low-velocity impact energy introduced damage at different locations. The experimental modal frequencies and the corresponding mode shapes for the first 10 flexural modes are obtained by using a scanning laser vibrometer with a PZT actuator. From the mode shapes, mode shape curvatures are obtained by using a central difference approximation. In order to exclude the influence of measurement noise on the modal data and misleading damage indices, it is proposed to use the average sum of mode shape curvature squares for each mode. With the example of the beams with free-free and clamped boundary conditions, it is shown that the mode shape curvature squares can be used to detect damage in the structures. The extent of low-velocity impact introduced damage is identified via the modal frequencies by using mixed numerical-experimental technique. The method is based on the minimization of the discrepancy between the numerically calculated and the experimentally measured frequencies. The numerical frequencies are calculated by employing a finite-element model for beam with introduced damage. Further, by using the response surface approach, a relationship (second-order polynomial function) between the modal frequencies and the damage extent is constructed. The damage extent is obtained by solving the minimization problem
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