Journal of Mechanical Science and Technology

The Korean Society of Mechanical Engineers (대한기계학회)
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Dynamic Characteristics of a Damaged Plate

  • Lee, Usik (Department of Mechanical Engineering Inha University)
  • Published : 2001.10.01
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Abstract

It is very important to well understand the dynamic characteristics of damaged structures to successfully develop or to choose a most appropriate structural damage identification method (SDIM) as the means of non-destructive testing. In this pope., the dynamic equation of motion for damaged plates is derived by introducing a damage distribution function, which may characterize the effective state of structural damages. It is found that structural damages may induce the coupling between modal coordinates. The effects of damages on the vibration characteristics of a plate depending on their locations, sizes, and magnitudes are numerically investigated in a systematic way. The numerical investigations are also given to the effects of damage-induced modal coupling on the changes in vibration characteristics and to the minimum number of natural modes required to predict sufficiently accurate vibration characteristics of damaged plates.

Keywords

References

  1. Banks, H. T., Inman, D. J., Leo, D. J., and Wang, Y., 1996, 'An Experimentally Validated Damage Detection Theory in Smart Structures,' Journal of Sound and Vibration, Vol. 191, No. 5, pp. 859-880 https://doi.org/10.1006/jsvi.1996.0160
  2. Blevins, R. D., 1979, Formulas for Natural Frequency and Mode Shape, Van Nostrand Reinhold Co., New York
  3. Chen, W. H., and Chen, P. Y., 1984, 'A Hybrid -Displacement Finite Element Model for the Bending Analysis of Thin Cracked Plates,' International Journal of Fracture, Vol. 24, pp. 83-106 https://doi.org/10.1007/BF00028054
  4. Davini, C, Morassi, A., and Rovere, N., 1995, 'Modal Analysis of Notched Bars: Tests and Comments on the Sensitivity of an Identification Technique,' Journal of Sound and Vibration, Vol. 179, No. 3, pp. 513-527 https://doi.org/10.1006/jsvi.1995.0033
  5. Dimarogonas, A. D., 1996, 'Vibration of Cracked Structures: A State of the Art Review,' Engineering Fracture Mechanics. Vol. 55, No. 5, pp. 831-857 https://doi.org/10.1016/0013-7944(94)00175-8
  6. Doebling, S. W., Farrar, C. R., and Prime, M. B., 1998, 'A Summary Review of Vibration-based Damage Identification Method,' The Shock and Vibration Digest, Vol. 30, No. 2, pp. 91-105 https://doi.org/10.1177/058310249803000201
  7. Dowell, E. H., 1975, Aeroelasticity of Plates and Shells, Noordhoff International Pub., Leyden, The Netherlands
  8. Gudmundson, P., 1982, 'Eigenfrequency Changes of Structures Due to Cracks, Notches or Other Geometrical Changes,' Journal of the Mechanics and Physics of Solids, Vol. 30, No. 5, pp. 339-353 https://doi.org/10.1016/0022-5096(82)90004-7
  9. Khadem, S. E., and Rezaee, M., 2000, 'An Analytical Approach for Obtaining the Location and Depth of an All-over Part-through Crack on Externally In-plane Loaded Rectangular Plate Using Vibration Analysis,' Journal of Sound and Vibration, Vol. 230, No. 2 pp. 291-308 https://doi.org/10.1006/jsvi.1999.2619
  10. Lee, H. P., and Lim, S. P., 1993, 'Vibration of Cracked Rectangular Plates Including Transverse Shear Deformation and Rotary Inertia,' Computers & Structures, Vol. 49, pp. 715-718 https://doi.org/10.1016/0045-7949(93)90074-N
  11. Lee, U., Chang, J., and Kim, N., 2000, 'Structural Micro-Damage Identification,' AIAA Paper 2000-1503
  12. Leung, A. Y. T., and Su, R. K. L., 1996, 'Fractal Two-Level Finite Element Analysis of Cracked Reissners' Plate,' Thin-Walled Structures, Vol. 24, pp. 315-334 https://doi.org/10.1016/0263-8231(95)00044-5
  13. Luo, H., and Hanagud, S., 1997, 'An Integral Equation for Changes in the Structural Dynamics Characteristics of Damaged Structures,' International Journal of Solids and Structures, Vol. 34, No. 35/36, pp. 4557-4579 https://doi.org/10.1016/S0020-7683(97)00038-3
  14. Lynn, P. P., and Kumbasar, N., 1967, 'Free Vibrations of Thin Rectangular Plates Having Narrow Cracks with Simply Supported Edges,' Development in Mechanics, Vol. 4, pp. 911-928
  15. Meirovitch, L., 1980, Computational Methods in Structural Dynamics, Sijthoff & Noordhoff, Alphen aan den Rijin, The Netherlands
  16. Pandey, A. K., Biswas, M., and Samman, M. M., 1991, 'Damage Detection from Changes in Curvature Mode Shapes,' Journal of Sound and Vibration, Vol. 145, No. 2, pp. 321-332 https://doi.org/10.1016/0022-460X(91)90595-B
  17. Sato, H., 1983, 'Free Vibration of Beams with Abrupt Changes of Cross-Section,' Journal of Sound and Vibration, Vol. 89, No. 1, pp. 59-64 https://doi.org/10.1016/0022-460X(83)90910-0
  18. Stahl, B., and Keer, L. M., 1972, 'Vibration and Stability of Cracked Rectangular Plates,' International Journal of Solids and Structures, Vol. 8, pp. 69-91 https://doi.org/10.1016/0020-7683(72)90052-2
  19. Weissenburger, J. T., 1968, 'Effect of Local Modifications on the Vibration Characteristics of Linear Systems,' Journal of Applied Mechanics, Vol. 35, pp. 327-335
  20. Yu, Y. Y., 1996, Vibration of Elastic Plates, Springer-Verlag, New York
  21. Yuen, M. M. F., 1985, 'A Numerical Study of the Eigenparameters of a Damaged Cantilever,' Journal of Sound and Vibration, Vol. 103, pp. 301-310 https://doi.org/10.1016/0022-460X(85)90423-7