A study of vibration of geometrically segmented beams with and without crack

International Journal of Solids and Structures

Volumn 37, Issue 5, 1999, Pages 761-779

  Chaudhari, T D ^a   Maiti, S K ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY BOMBAY   (India)

Author keywords

Cantilever; Crack; Euler Bernoulli beam; Finite element; Vibration

Indexed keywords

CRACK PROPAGATION; FINITE ELEMENT METHOD; INVERSE PROBLEMS; MATHEMATICAL MODELS; NATURAL FREQUENCIES; STRUCTURAL ANALYSIS; VIBRATIONS (MECHANICAL);

EULER-BERNOULLI BEAMS;

CANTILEVER BEAMS;

EID: 0033883093     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7683(99)00054-2     Document Type: Article

References (22)

1. Adams, R.D., Walton, D., Flitcroft, J.E., Short, D., 1975. Vibration testing as a nondestructive test tool for composite materials. Composite Reliability ASTM STP 580, 159-175.
2. Anifantis, N., Dimarogonas, A., 1983. Stability of columns with a single crack subjected to follower and vertical loads. International Journal of Solids and Structures 19, 281-291.
3. Auciello, N.M., Ercolano, A., 1997. Exact solution for the transverse vibration of a beam, a part of which is a taper beam and other part is a uniform beam. International Journal of Solids and Structures 34, 2115-2129.
4. Bathe, K.J., 1990. Finite Element Procedures in Engineering Analysis. Prentice Hall of India, New Delhi.
5. Carnegie, W., Thomas, J., 1967. Natural frequencies of long tapered cantilevers. The Aeronautical Quarterly 18, 309-320.
6. Cawley, P., Adams, R.D., 1979. The location of defects in structure from measurements of natural frequencies. Journal of Strain Analysis 14, 49-57.
7. Conway, H.D., Dubil, J.F., 1965. Vibration frequencies of truncated-cone and wedge beams. ASME Journal of Applied Mechanics 32, 932-934.
8. Dimarogonas, A.D., 1987. Modelling damaged structural members for vibration analysis. Journal of Sound and Vibration 112, 541-543.
9. Gaines, J.H., Volterra, E., 1966. Transverse vibrations of cantilever bars of variable cross-section. Journal of Acoustical Society of America 39, 674-679.
10. Liang, R.Y., Choy, F.K., Hu, J., 1991. Detection of cracks in beam structures using measurements of natural frequencies. Journal of the Franklin Institute 328, 505-518.
11. Mabie, H.H., Rogers, C.B., 1968. Transverse vibrations of tapered cantilever beams with end support. Journal of Acoustical Society of America 44, 1739-1741.
12. Maiti, S.K., 1996. Finite Element Package for Stress and Vibration Analysis. Mechanical Engineering Department. Indian Institute of Technology, Bombay, pp. 8-74 MED-SKM-TR-96-01.
13. Martin, A.I., 1956. Some integrals relating to the vibration of a cantilever beam and approximation for the effect of taper on over-tone frequencies. The Aeronautical Quarterly 7, 120-128.
14. Naguleswaran, S., 1994. A direct solution for transverse vibration of Euler-Bernoulli wedge and cone beams. Journal of Sound and Vibration 172, 289-304.
15. Nandwana, B.P., 1998. On foundation for detection of crack based on measurement of natural frequencies. Ph.D. Thesis, Mechanical Engineering Department, Indian Institute of Technology, Bombay.
16. Nandwana, B.P., Maiti, S.K., 1997a. Detection of location and size of a crack in stepped cantilever beams based on measurements of natural frequencies. Journal of Sound and Vibration 203, 435-446.
17. Nandwana, B.P., Maiti, S.K., 1997b. Vibration based detection of location and size of edge crack in beams on multiple supports. In: Proceedings of the 9th International Conference on Fracture. Pergamon Press, Oxford, pp. 2603-2610.
18. Nandwana, B.P., Maiti, S.K., 1997c. Modelling of vibration of beam in presence of inclined edge and internal crack for its possible detection based on frequency measurements. Engineering Fracture Mechanics 58 (3), 193-205.
19. Ostachowicz, W.M., Krawczuk, M., 1991. Analysis of the effect of cracks on the natural frequencies of a cantilever beam. Journal of Sound and Vibration 150, 191-201.
20. Rao, J.S., 1965. The fundamental flexural vibration of a cantilever beam of rectangular cross-section with uniform taper. The Aeronautical Quarterly 16, 139-148.
21. Rizos, P.F., Aspragathos, N., Dimarogonas, A.D., 1990. Identification of crack location and magnitude in a cantilever beam from the vibration modes. Journal of Sound and Vibration 138, 381-388.
22. Wang, H.C., 1967. Generalised hypergeometric function solutions on the transverse vibration of a class of non-uniform beams. ASME Journal of Applied Mechanics 34, 702-708.