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During the last decades a great variety of methods have been proposed for damage detection by using the dynamic structure characteristics, however, most of them require modal data of the structure for the healthy state as a reference. In this paper the applicability of the mode shape curvature squares determined from only the damaged state of the structure for damage detection in a beam structure is studied. To establish the method, two aluminium beams containing different-size mill-cut damage at different locations are tested by using the experimentally measured modal data. The experimental modal frequencies and the corresponding mode shapes 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. 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. Further, the extent of a mill-cut damage is identified via modal frequencies by using a mixed numerical-experimental technique. The method is based on the minimization of the discrepancy between the numerically calculated and experimentally measured frequencies.

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During the last two decades structural damage identification using dynamic parameters of the structure has become an important research area for civil, mechanical, and aerospace engineering communities. The basic idea of the vibration‐based damage detection methods 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. To establish the method, two aluminium beams containing different sizes of mill‐cut damage at a single location as well as two aluminium beams containing different sizes of mill‐cut damage at multiple locations are examined. The experimental modal frequencies and the corresponding mode shapes for the first 15 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 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 mill‐cut 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. Santrauka Tyrimo metu buvo ieškomos sijines konstrukcijos pažeidimo frezuojant vietos, apimtis ir pažeidimo dydis pagal atlikto vibraciju eksperimento dinamines charakteristikas. Pažeidimo padetis ir apimtis buvo nustatomi pagal išlinkio formos virpesiu kvadrato dydi. Pažeidimo dydis buvo nustatomas skaitiniu‐eksperimentiniu metodu, taikant modalinius dažnius. Šio metodo efektyvumas ir patikimumas parodytas tiriant dvi aliuminio sijas, kurios buvo pažeistos frezos vienoje vietoje ir kurios buvo pažeistos skirtingose vietose.