Abstract




 
   

IJE TRANSACTIONS B: Applications Vol. 28, No. 2 (February 2015) 321-329   

downloaded Downloaded: 459   viewed Viewed: 2513

  A SIMPLE METHOD FOR MODELING OPEN CRACKED BEAM
 
A. Nakhaei, M. Dardel, M. Ghasemi and M. Pashaei
 
( Received: March 24, 2014 – Accepted: November 13, 2014 )
 
 

Abstract    Abstract A simple method is proposed to model the open cracked beam structures. In this method, crack is modeled as a beam element. Hence cracked beam can be assumed to be a beam with stepped cross sections, and problem of determining natural frequency and mode shape of cracked beam, can be solved as determining these characteristics for a beam with different length and cross section. With this work, it is not necessary to model crack as lumped flexibility model in according to fracture mechanics and related sciences to obtain crack stiffness, and use this spring model of crack for further analysis.

 

Keywords    Keywords: Crack, lumped stiffness model, step beam, natural frequency, mode shape.

 

چکیده    چكيده یک روش ساده برای مدل‌سازی نرک باز در ساختارهای به شکل تیر ارایه شده است. در این روش ترک به صورت یک المان تیر مدل‌سازی می‌شود. از این رو تیر به صورت یک تیر با تغییر پله‌ای در سطح مقطع در نظر گرفته می‌شود، و مساله تعیین فرکانس طبیعی و شکل تیر به صورت حل ایت مشخصه‌ها برای یک تیر با طول و سطح مقطع متفاوت قابل حل خواهد بود. با این کار نیاز به مدل‌سازی تیر به صورت تیر با انعطاف‌پذیری متمرکز بر طبق تئوری شکست و یا علوم مربوطه برای تعیی سفتی ترک و استفاده از این مدل فنر برای تحلیل‌های بعدی مربوطه نخواهد بود.

References   

 

1.     Dimarogonas, A.D., "Vibration of cracked structures: A state of the art review", Engineering fracture mechanics,  Vol. 55, No. 5, (1996), 831-857.

2.     Haisty, B. and Springer, W., "A general beam element for use in damage assessment of complex structures", Journal of Vibration and Acoustics,  Vol. 110, No. 3, (1988), 389-394.

3.     Gounaris, G. and Dimarogonas, A., "A finite element of a cracked prismatic beam for structural analysis", Computers & Structures,  Vol. 28, No. 3, (1988), 309-313.

4.     Ibrahim, F.K., "An elastoplastic cracked-beam finite element for structural analysis", Computers & Structures,  Vol. 49, No. 6, (1993), 981-988.

5.     Kirmser, P.G., "The effects of discontinuities on the natural frequency of beams, The College,(1945).

6.     Dimarogonas, A.D., "Vibration engineering, West Publishing Company,  (1976).

7.     Christides, S. and Barr, A., "One-dimensional theory of cracked bernoulli-euler beams", International Journal of Mechanical Sciences,  Vol. 26, No. 11, (1984), 639-648.

8.     Christides, S. and Barr, A., "Torsional vibration of cracked beams of non-circular cross-section", International Journal of Mechanical Sciences,  Vol. 28, No. 7, (1986), 473-490.

9.     Reddy, J., "Energy and variational methods, John Wiley, New York,  (1984).

10.   Barr, A., "An extension of the hu-washizu variational principle in linear elasticity for dynamic problems", Journal of Applied Mechanics,  Vol. 33, No. 2, (1966), 465-465.

11.   Shen, M.-H. and Chu, Y., "Vibrations of beams with a fatigue crack", Computers & Structures,  Vol. 45, No. 1, (1992), 79-93.

12.   Shen, M.-H. and Pierre, C., "Natural modes of bernoulli-euler beams with symmetric cracks", Journal of sound and vibration,  Vol. 138, No. 1, (1990), 115-134.

13.   Shen, M.-H. and Pierre, C., "Free vibrations of beams with a single-edge crack", Journal of sound and vibration,  Vol. 170, No. 2, (1994), 237-259.

14.   Chondros, T. and Dimarogonas, A., "Vibration of a cracked cantilever beam", Journal of Vibration and Acoustics,  Vol. 120, No. 3, (1998), 742-746.

15.   Chondros, T., Dimarogonas, A. and Yao, J., "A continuous cracked beam vibration theory", Journal of sound and vibration,  Vol. 215, No. 1, (1998), 17-34.

16.   Chondros, T., Dimarogonas, A. and Yao, J., "Longitudinal vibration of a bar with a breathing crack", Engineering fracture mechanics,  Vol. 61, No. 5, (1998), 503-518.

17.   Chondros, T., Dimarogonas, A. and Yao, J., "Longitudinal vibration of a continuous cracked bar", Engineering fracture mechanics,  Vol. 61, No. 5, (1998), 593-606.

18.   Gudmundson, P., "Eigenfrequency changes of structures due to cracks, notches or other geometrical changes", Journal of the Mechanics and Physics of Solids,  Vol. 30, No. 5, (1982), 339-353.

19.   Banks, H., Emeric, P. and Plancke, L., "Modeling of nonsymmetrical damage in plate-like structures", Mathematical and Computer Modelling,  Vol. 26, No. 3, (1997), 55-65.

20.   Plakhtienko, N. and Yasinskii, S., "Resonance of second order in vibrations of a beam containing a transverse crack", Strength of materials,  Vol. 27, No. 3, (1995), 146-152.

21.   Ballo, I., "Non-linear effects of vibration of a continuous transverse cracked slender shaft", Journal of sound and vibration,  Vol. 217, No. 2, (1998), 321-333.

22.   Jassim, Z., Ali, N., Mustapha, F. and Abdul Jalil, N., "A review on the vibration analysis for a damage occurrence of a cantilever beam", Engineering Failure Analysis,  Vol. 31, No., (2013), 442-461.

23.   AL-Shudeifat, M.A., "On the finite element modeling of the asymmetric cracked rotor", Journal of sound and vibration,  Vol. 332, No. 11, (2013), 2795-2807.

24.   Gomes, H.M. and de Almeida, F.J.F., "An analytical dynamic model for single-cracked beams including bending, axial stiffness, rotational inertia, shear deformation and coupling effects", Applied Mathematical Modelling,  Vol. 38, No. 3, (2014), 938-948.

25.   Caddemi, S. and Morassi, A., "Multi-cracked euler–bernoulli beams: Mathematical modeling and exact solutions", International Journal of Solids and Structures,  Vol. 50, No. 6, (2013), 944-956.

26.   Dixit, A. and Hodges, D.H., "A general damage theory: Solution of nth-order equations using Unified Framework ", Mechanics Research Communications,  Vol. 38, No. 7, (2011), 486-493.

27.   Rakideh, M., Dardel, M. and Pashaei, M., "Crack detection of timoshenko beams using vibration behavior and neural network", International Journal of Engineering-Transactions C: Aspects,  Vol. 26, No. 12, (2013), 1433.

28.   Broek, D., "Elementary engineering fracture mechanics, Springer,  (1986).

29.   Ostachowicz, W. and Krawczuk, M., "Analysis of the effect of cracks on the natural frequencies of a cantilever beam", Journal of sound and vibration,  Vol. 150, No. 2, (1991), 191-201.

30.   Rao, S.S., "Vibration of continuous systems, John Wiley & Sons,  (2007).

31.   Khaji, N., Shafiei, M. and Jalalpour, M., "Closed-form solutions for crack detection problem of timoshenko beams with various boundary conditions", International Journal of Mechanical Sciences,  Vol. 51, No. 9, (2009), 667-681.

32.           Lin, H.-P., "Direct and inverse methods on free vibration analysis of simply supported beams with a crack", Engineering structures,  Vol. 26, No. 4, (2004), 427-436.





International Journal of Engineering
E-mail: office@ije.ir
Web Site: http://www.ije.ir