Transactions of the Korean Society of Mechanical Engineers A (대한기계학회논문집A)

The Korean Society of Mechanical Engineers (대한기계학회)
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Crack Identification Using Optimization Technique

수학적 최적화기법을 이용한 결함인식 연구

  • Published : 2000.01.01
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Abstract

It has been established that a crack has an important effect on the dynamic behavior of a structure. This effect depends mainly on the location and depth of the crack. To identify the location and depth of a crack in a structure. Nikolakopoulos et. al. used the intersection point of the superposed contours that correspond to the eigenfrequency caused by the crack presence. However the intersecting point of the superposed contours is not only difficult to find but also incorrect to calculate. A method is presented in this paper which uses optimization technique for the location and depth of the crack. The basic idea is to find parameters which use the structural eigenfrequencies on crack depth and location and optimization algorithm. With finite element model of the structure to calculate eigenfrequencies, it is possible to formulate the inverse problem in optimization format. Method of optimization is augmented lagrange multiplier method and search direction method is BFGS variable metric method and one dimensional search method is polynomial interpolation.

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References

  1. Natke, H. G., 1988, ' Application of System Identification in Engineering,' CISM CAL-296
  2. Chondros, T. C. and Dimarogonas, A. D., 1979, 'Identification of Cracks in Circular Plates Welded at the Contour,' In: ASME Design Engineering Technical Conference, St. Louis
  3. Chondros, T. C. and Dimarogonas, A. D., 1980, 'Identification of cracks in welded joints of complex structures,' Journal of Sound and Vibration 69, pp. 531-538 https://doi.org/10.1016/0022-460X(80)90623-9
  4. Gounaris, G. D. and Dimarogonas, A. D., 1988, 'A finite element of a cracked prismatic beam in structural analysis,' Computer and Structure 28, pp. 309-313 https://doi.org/10.1016/0045-7949(88)90070-3
  5. Gounaris, G. D. and Papazoglou, V., 1992, 'Three-dimensional effects on the natural vibration of cracked Timoshenko beams in water,' Computer and Structure 42, pp. 769-779 https://doi.org/10.1016/0045-7949(92)90188-6
  6. Inagaki, T., Kanki, H. and Shiraki, K., 1981, 'Transverse vibrations of a general cracked rotor bearing system,' Journal of Mechanical Design 104, pp. 1-11
  7. Leung, P. S., 1992, 'The effects of a transverse Crack on the dynamics of a circular shaft,' In: Rotor dynamics '92. Int. Conf. on Rotating Machine Dynamics. Venice
  8. Anifantis, N., Rizos P. and Dimarogonas, A. D., 1987, 'Identification of cracks on beams by vibration analysis,' In: 11th Biennial ASME Conference on Mechanical Vibration and Noise, Boston
  9. Dimarogonas, A. D. and Massouros, G., 1981, 'Torsional vibrations of a shaft with a circumferential crack,' Engineering Fracture Mechanical. 15, pp. 439-444
  10. Nikolakopoulos, H. G., Katsareas, D. E. and Papadopoulos, C. A., 1997, 'Computer & Structures,' Vol. 64, No. 1-4, pp. 389-406 https://doi.org/10.1016/S0045-7949(96)00120-4
  11. Furukawa, T. and Yagawa, G., 1995, 'Computational Mechanics '95, Springer,' pp. 122-127
  12. Ogawa, H. and Oja, E., 1986, 'Projection Filter, Wiener Filter, and Karhunen-Loeve Subspaces in Digital Image Restoration,' Journal of Mathematical Analysis and Application, Vol.114, pp. 37-51 https://doi.org/10.1016/0022-247X(86)90063-6
  13. Papadopoulos, C. A. and Dimarogonas, A. D., 1988, 'Coupled longitudinal and bending vibrations of a cracked shaft,' Journal of Vibration Acoustic Stress Reliability Design 110, pp. 1-8
  14. Tada, H., 1973, The Stress Analysis of Cracks Handbook, Del Research Corporation. PA
  15. Hasanov, A., 1994, 'Computational aspects of an inverse diagnostic problem for an elastoplastic medium,' WCCM III. 2-G10-3, pp. 982-983
  16. Tarantola, A., 1987, Inverse problem theory, Elsevier
  17. Vanderplaats, G. N., 1993, Numerical optimization techniques for engineering design with applications, Mcgraw-hill international editions
  18. Dimarogonas, A. D., 1976, Vibration Engineering, West. St Paul, MN