Study of the Effect of an Open Transverse Crack on the Vibratory Behavior of Rotors Using the h-p Version of the Finite Element Method
Subject Areas : Mechanical EngineeringF Ahmed 1 , H Abdelhamid 2 , B Brahim 3 , S Ahmed 4
1 - IS2M Laboratory, Faculty of Technology, University of Tlemcen, Algeria
2 - IS2M Laboratory, Faculty of Technology, University of Tlemcen, Algeria
3 - IS2M Laboratory, Faculty of Technology, University of Tlemcen, Algeria
4 - IS2M Laboratory, Faculty of Technology, University of Tlemcen, Algeria
Keywords:
Abstract :
[1] Gallagher R.H., 1975, Finite Element Analysis: Fundamentals, Prentice Hall Civil Engineering and Engineering Mechanics, Pearson College Div.
[2] Zienkiewicz C., 1977, The Finite Element Method, McGraw-Hill.
[3] Szabo B.A., 1979, Some recent developments in the finite element analysis, Computers & Mathematics Applications, 5(2): 99-115.
[4] Babuška I., Szabo B.A., Katz I.N., 1981, The p-version of the finite element method, SIAM Journal on Numerical Analysis 18(3): 515-545.
[5] Meirovitch L., Bahuh H., 1983, On the inclusion principle for the hierarchical finite element method, International Journal for Numerical Methods in Engineering 19: 281-291.
[6] Gui W., Babuška I., 1986, The h, p and h-p versions of the finite element method in 1 dimension, part I, The error analysis of the p-version, Numerische Mathematik 49(6): 577-612.
[7] Babuška I., Suri M., 1987, The h-p version of the finite element method with quasi uniform meshes, Mathematical Modeling and Numerical Analysis 21(2): 199-238.
[8] Babuška I., Guo B.Q., 1992, The h, p and h-p version of the finite element method: Basis theory and applications, Advances in Engineering Software 15 (3-5): 159-174.
[9] Boukhalfa A., Hadjoui A., 2010, Free vibration analysis of an embarked rotating composite shaft using the h-p version of the FEM, Latin American Journal of Solids and Structures 7(2): 105-141.
[10] Saimi A., Hadjoui A., 2016, An engineering application of the h-p version of the finite elements method to the dynamics analysis of a symmetrical on-board rotor, European Journal of Computational Mechanics 25(5): 1779-7179.
[11] Wauer J., 1990, Dynamics of cracked rotors: literature survey, Applied Mechanics Reviews 43(1): 13-17.
[12] Dimarogonas A.D., 1996, Vibration of cracked structures: a state of the art review, Engineering Fracture Mechanics 55(5): 831-857.
[13] Sabnavis G., Kirk R.G., Kasarda M., Quinn D.D., 2004, Cracked shaft detection and diagnostics: a literature review, The Shock and Vibration Digest 36(4): 287-296.
[14] Gasch R., 1993, A survey of the dynamic behavior of a simple rotating shaft with a transverse crack, Journal of Sound and Vibration 160: 313-332.
[15] Edwards S., Lees A. W., Friswell M. I., 1998, Fault diagnosis of rotating machinery, The Shock and Vibration Digest 30: 4-13.
[16] Davies W. G. R., Mayes I. W., 1984, The vibration behavior of a multi-shaft, multi-bearing system in the presence of a propagating transverse crack, Journal of Vibration, Acoustics, Stress, and Reliability in Design 106: 146-153.
[17] Chasalevris A.C., Papadopoulos C.A., 2008, Coupled horizontal and vertical vibrations of a stationary shaft with two cracks, Journal of Sound and Vibration 309: 507-528.
[18] Mazanoglu K., Yesilyurt I., Sabuncu M., 2009, Vibration analysis of multiple-cracked non-uniform beams, Journal of Sound and Vibration 320(4–5): 977-989.
[19] Darpe A.K., Gupta K., Chawla A., 2004, Transient response and breathing behaviour of a cracked Jeffcott rotor, Journal of Sound and Vibration 272: 207-243.
[20] Petal T.H., Darpe A.K., 2008, Influence of crack breathing model on nonlinear dynamics of a cracked rotor, Journal of Sound and Vibration 311: 953-972.
[21] AL-Shudeifat M.A., Eric A., Butcher Carl R.S., 2010, General harmonic balance solution of a cracked rotor-bearing-disk system for harmonic and sub-harmonic analysis: Analytical and experimental approach, International Journal of Engineering Science 48: 921-935.
[22] Huang S.C., Huang Y.M., Shiah S.M., 1993, Vibration and stability of a rotating shaft containing a transverse crack, Journal of Sound Vibration 162: 387-401.
[23] Sinou J-J., 2007, Effects of a crack on the stability of a non-linear rotor system, International Journal of Non-Linear Mechanics 42(7): 959-972.
[24] Guo C., AL-Shudeifat M.A., Yan J., Bergman L.A., McFarland D.M., Butcher E.A., 2013, Stability analysis for transverse breathing cracks in rotor systems, European Journal of Mechanics and Solids 42: 27-34.
[25] AL-Shudeifat M.A., 2015, Stability analysis and backward whirl investigation of cracked rotors with time-varying stiffness, Journal of Sound and Vibration 348: 365-380.
[26] Dimarogonas A.D., Papadopoulos C.A., 1983, Vibration of cracked shafts in bending, Journal of Sound and Vibration 91(4): 583-593.
[27] Silani M., Ziaei-Rad S., Talebi H., 2013, Vibration analysis of rotating systems with open and breathing cracks, Applied Mathematical Modeling 37(24): 9907-9921.
[28] AL-Shudeifat M.A., 2013, On the finite element modeling of an asymmetric cracked rotor, Journal of Sound and Vibration 332(11): 2795-2807.
[29] Qinkai H., Fulei C., 2013, Dynamic response of cracked rotor-bearing system under time-dependent base movements, Journal of Sound and Vibration 332(25): 6847-6870.
[30] Sinou J-J., Lees A.W., 2005,The influence of cracks in rotating shafts, Journal of Sound and Vibration 285(4-5): 1015-1037.
[31] AL-Shudeifat M.A., Butcher E.A., 2011, New breathing functions for the transverse breathing crack of the cracked rotor system: approach for critical and subcritical harmonic analysis, Journal of Sound and Vibration 330(3): 526-544.
[32] Guo C., AL-Shudeifat M.A., Yan J., Bergman L.A., McFarland D.M., Butcher E.A., 2013, Stability analysis for transverse breathing cracks in rotor systems, European Journal of Mechanics and Solids 42: 27-34.
[33] Pilkey W.D., 2002, Analysis and Design of Elastic Beams, John Wiley and Sons, New York.
[34] Bardell N.S., 1996, An engineering application of the h-p version of the finite element method to the static analysis of a Euler-bernoulli beam, Computers & Structures 59(2): 195-211.