Abstract
The use of modal-analysis techniques as nondestructive methods for the detection of cracks in beams is a current field of interest for various researchers. However, an extensive search of the published literature shows that there is very little information on experimental results, thus making it almost impossible for theoretical researchers to use published experimental data to validate their models.
The authors, who are currently working in the field of crack detection through modal analysis, performed an extensive experimental dynamic analysis of free-free beams with the objective of validating theoretical techniques, under development, for the prediction of the location and depth of cracks in straight beams. This paper describes the first part of the authors' work. The experimental techniques used are described and results obtained for various locations and depths of cracks in a straight free-free beam are presented.
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Abbreviations
- a a′ :
-
crack-propagation line
- A c :
-
area of crack
- d :
-
beam depth
- E :
-
Young's modulus
- H :
-
code letter indicating that measurements were obtained for out of plane flexural vibrations (bending in the plane of higher second moment of area of cross section of beam)
- L :
-
length of beam
- L 1 :
-
crack location along the length of the beam
- p :
-
crack depth
- P y :
-
code letter indicating that the crack propagates in the direction of the y axis
- P z :
-
code letter indicating that the crack propagates in the direction of the z axis
- Q i :
-
ratio ω ci /ω i
- R i :
-
ratio δω i /ω i
- t :
-
beam thickness
- V :
-
code letter indicating that measurements were obtained for in-plane flexural vibrations (bending in the plane of lower second moment of area of cross section of beam)
- ν:
-
Poisson's coefficient
- ω i :
-
ith natural bending frequency, in the plane of measurements, of noncracked beam
- ω i :
-
ith natural bending frequency, in the plane of measurements, of cracked beam
- δω i :
-
ω i -ω ci
- ω hi :
-
highest value of theith measured natural frequency
- ωℓi :
-
lowest value of theith measured natural frequency
- ϱ:
-
mass density
- λ:
-
small arbitrary quantity
References
Nichols, R.W., “Advances in Non-Destructive Examinations for Structural Integrity,” Applied Science Publishers (1972).
Rolfe, S. and Barson, J., “Fracture and Fatigue Control in Structures: Applications of Fracture Mechanics,” Prentice-Hall (1977).
Dimarogonas, A.D. and Chondros, T.G., “Identification of Cracks in Welded Joints of Complex Structures,” J. Sound and Vib.,69 (4), (1980).
Ju, F.D., Wong, E.T. and Paez, T.L., “Modal Method in Diagnosis of Fracture Damage in Simple Structures,” Productive Applications of Mechanical Vibrations, ASME Publications (1982).
Freund, L.B. and Hermann, G., “Dynamic Fracture of a Beam in Plane Bending,” Trans. ASME, J. Appl. Mech. (1986).
Gomes, A.J.M.A., “Identification of Cracks Through Dynamic Analysis” (in Portuguese), MSc Thesis, Tech. Univ. of Lisbon (1987).
Wendtland, D., “Aunderung der Biegeeigenfrequenzen Einer Idealisierten Schaufel durch Risse,” PhD Thesis, Univ. of Karlsruhe (1973).
Gomes, A.J.M.A. and Montalvao e Silva, J.M., “On the Prediction of Crack Location and Depth in Structural Components,” paper in preparation.
Ewins, D.J., “Modal Testing: Theory and Practice,”Wiley, New York (1984).
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Montalvão E Silva, J.M., Aráujo Gomes, A.J.M. Experimental dynamic analysis of cracked free-free beams. Experimental Mechanics 30, 20–25 (1990). https://doi.org/10.1007/BF02322697
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DOI: https://doi.org/10.1007/BF02322697