Identification of Cracks in Rotors and Other Structures by Vibration Analysis
The question of crack detection from dynamic measurements is further extended and discussed in Chap. 7. A general stiffness matrix for cracked structural members is introduced, to model the respective dynamic system. This stiffness matrix can be further u
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Identification of Cracks in Rotors and Other Structures by Vibration Analysis
Abstract The question of crack detection from dynamic measurements is further extended and discussed in Chap. 7. A general stiffness matrix for cracked structural members is introduced, to model the respective dynamic system. This stiffness matrix can be further utilized for static, dynamic or stability analysis of a structure with cracked members of rectangular or circular cross-section. Offdiagonal terms indicate vibration coupling. The change in dynamic response is analytically evaluated for simple systems and by means of approximate methods for more complicated ones. The outlined procedure can be used for engineering analysis in two ways: (a) as a design tool, to assist in structural optimization with the objective of achieving certain specific dynamic characteristics; and (b) as a maintenance and inspection tool, to identify structural flaws, such as cracks, by linking the variations in service of the structure’s natural frequencies to structural changes due to the cracks.
7.1 Flexibility Matrix of Cracked Structural Members In the previous chapter it was shown that the presence of a crack on a rotating shaft may change to a measurable, even substantial, extent its dynamic characteristics. A crack on a structural member introduces a local flexibility, which is a function of the crack depth. This flexibility changes the dynamic behavior of the system and its stability characteristics. In this chapter, the problem of identification of the crack from the resulting change in the dynamic behavior of the system containing the crack will be examined. It must be emphasized that nonpropagating cracks will be examined.
A. D. Dimarogonas et al., Analytical Methods in Rotor Dynamics, Mechanisms and Machine Science 9, DOI: 10.1007/978-94-007-5905-3_7, Springer Science+Business Media Dordrecht 2013
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7 Identification of Cracks in Rotors and Other Structures
The local flexibility of a cracked beam was studied by Irwin [1], who related this flexibility (compliance) to the stress intensity factor. The effect of the local flexibility of a cracked column upon its buckling load was studied by Liebowitz et al. [2, 3] and Ocamura [4]. These authors identified the compliance of a cracked column to a bending moment. Rice and Levy [5] recognized coupling between bending and extensional compliance of a cracked column in compression. The effect of cracks upon the dynamic behavior of cracked beams was studied by Dimarogonas [6] and by Chondros and Dimarogonas [7, 8]. The effect of peripheral cracks upon the torsional vibration of a rod of circular cross-section was studied by Dimarogonas and Massouros [9]. The investigation of cracked rotors behavior in torsional vibration and the development of crack detection methods for rotating shafts were initiated at about 1970. In a literature survey on the dynamics of cracked rotors by Wauer [10] it is stated that obviously the first work was done by the General Electric Company. The problem was further
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