A Simple Finite Element Procedure for Free Vibration and Buckling Analysis of Cracked Beam-Like Structures
محورهای موضوعی : EngineeringM.R Shirazizadeh 1 , H Shahverdi 2 , A Imam 3
1 - Department of Mechanical and Aerospace Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
2 - Department of Aerospace Engineering and Center of Excellence in Computational Aerospace, Amirkabir University of Technology, 424 Hafez Avenue, Tehran 15875-4413, Iran
3 - Department of Mechanical and Aerospace Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
کلید واژه: Modal Analysis, Cracked beam, Buckling load, F.E.M,
چکیده مقاله :
In this study, a novel and very simple finite element procedure is presented for free vibration and buckling analysis of slim beam-like structures damaged by edge cracks. A cracked region of a beam is modeled using a very short element with reduced second moment of area (I). For computing reduced Iin a cracked region, the elementary theory of bending of beams and local flexibility approach are used. The method is able to model cracked beam-columns by using ordinary beam elements. Therefore, it is possible to solve these problems with much less computational costs compared to 2D and 3D standard FE models. Numerical examples are offered to demonstrate the efficiency and effectiveness of the presented method.
[1] Kirmsher P.G., 1944, The effect of discontinuity on natural frequency of beams, Proceedings of the American Society of Testing and Materials 44: 897-904.
[2] Thomson W.J., 1943, Vibration of slender bars with discontinuities in stiffness, Journal of Applied Mechanics 17: 203-207.
[3] Zheng T., Ji T., 2012, An approximate method for determining the static deflection and Natural frequency of a
cracked beam, Journal of Sound and Vibration 331: 2654-2670.
[4] Okamura H., Liu H.W., Chorn-Shin C., Liebowitz H., 1969, A cracked column under compression, Engineering Fracture Mechanics 1: 547-564.
[5] 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.
[6] 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.
[7] Zheng D.Y., Fan S.C., 2003, Vibration and stability of cracked hollow-sectional beams, Journal of Sound and Vibration 267: 933-954.
[8] Yazdchi K., Gowhari Anaraki A.R., 2008, Carrying capacity of edge-cracked columns under concentric vertical loads, Acta Mechanica 198: 1-19.
[9] Liu H.W., Chu C.S., Liebowitz H., 1973, Cracked columns under compression fixed ends, Engineering Fracture
Mechanics 3: 219-230.
[10] Shirfin E.I., Ruotolo R., 1999, Natural frequencies of a beam with an arbitrary number of cracks, Journal of Sound
and Vibration 222: 409-423.
[11] Li Q.S., 2001, Buckling of multi-step cracked columns with shear deformation, Engineering Structures 23: 356-364.
[12] Douka E., Bamnios G., Trochidis A., 2004, A method for determining the location and depth of cracks in double-
cracked beams, Applied Acoustics 65: 997-1008.
[13] Fernandez Saez J., Rubio L., Navarro C., 1999, Approximate calculations of the fundamental frequency for bending
vibrations of cracked beams, Journal of Sound and Vibration 225: 345-352.
[14] Attar M.A., 2012, Transfer matrix method for free vibration analysis and crack identification of stepped beams with
multiple edge cracks and different boundary conditions, International Journal of Mechanical Sciences 57: 19-33.
[15] Shen M.H.H., Pierre C., 1990, Natural modes of bernoulli-euler beams with symmetric cracks, Journal of Sound and Vibration 138: 115-134.
[16] Tharp T.M., 1987, A finite element for edge-cracked beam columns, International Journal of Numerical Methods in Engineering 24: 1941-1950.
[17] Gounaris G., Dimarogonas A., 1998, A finite element of a cracked prismatic beam for structural analysis, Computers
& Structures 28: 309-313.
[18] Ostachowicz W.M., Krawczuk M., 1990, Vibration analysis of a cracked beam, Computers & Structures 36: 245-250.
[19] Skrinar M., Plibersek T., 2007, New finite element for transversely cracked slender beams subjected to transverse
loads, Computational Materials Science 39: 250-260.
[20] Bouboulas A.S., Anifantis N.K., 2008, Formulation of cracked beam element for analysis of fractured skeletal structures, Engineering Structures 30: 894-901.
[21] Ansys Level 6.1, 1973, Data Preparation Manual, ANSYS, Canonsburg, Pennsylvania.
