Skip to main content
Log in

Dynamic characteristics of a damaged plate

  • Materials & Fracture · Solids & Structures · Dynamics & Control · Production & Design
  • Published:
KSME International Journal Aims and scope Submit manuscript

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 paper, 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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • 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.

    Article  Google Scholar 

  • Blevins, R. D., 1979,Formulas for Natural Frequency and Mode Shape, Van Nostrand Reinhold Co., New York.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Dimarogonas, A. D., 1996, “Vibration of Cracked Structures: A State of the Art Review,”Engineering Fracture Mechanics. Vol. 56, No. 5, pp. 831–857.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Dowell, E. H., 1975,Aeroelasticity of Plates and Shells, Noordhoff International Pub., Leyden, The Netherlands.

    MATH  Google Scholar 

  • 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.

    Article  MathSciNet  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

  • Lee, U., Chang, J., and Kim, N., 2000, “Structural Micro-Damage Identification,” AIAA Paper 2000-1503.

  • 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.

    Article  Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

  • 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.

    Google Scholar 

  • Meirovitch, L., 1980,Computational Methods in Structural Dynamics, Sijthoff & Noordhoff, Alphen aan den Rijin, The Netherlands.

    MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

  • Weissenburger, J. T., 1968, “Effect of Local Modifications on the Vibration Characteristics of Linear Systems,”Journal of Applied Mechanics, Vol. 35, pp. 327–335.

    MATH  Google Scholar 

  • Yu, Y. Y., 1996,Vibration of Elastic Plates, Springer-Verlag, New York.

    Google Scholar 

  • 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.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Usik Lee.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lee, U., Kim, N. & Kwon, OY. Dynamic characteristics of a damaged plate. KSME International Journal 15, 1408–1416 (2001). https://doi.org/10.1007/BF03185682

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03185682

Key Words

Navigation