Spectral finite element for vibration analysis of cracked viscoelastic Euler–Bernoulli beam subjected to moving load

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• 作者：Vahid Sarvestan ; Hamid Reza Mirdamadi ; Mostafa Ghayour ; Ali Mokhtari
• 刊名：Acta Mechanica
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：226
• 期：12
• 页码：4259-4280
• 全文大小：3,131 KB
• 参考文献：1.Timoshenko S., Young D.H., Weaver W.: Vibration Problems in Engineering, 4th edn. Wiley, New York (1974)
  2.Lee H.P.: Dynamic response of a beam with a moving mass. J. Sound Vib. 191, 289-94 (1996)CrossRef
  3.Hasheminejad S.M., Rafsanjani A.: Two-dimensional elasticity solution for transient response of simply supported beams under moving loads. Acta Mech. 217, 205-18 (2011)MATH CrossRef
  4.Fryba L.: Vibration of Solids and Structures Under Moving Loads, 3rd edn. Thomas Telford, Groningen (1999)CrossRef
  5.Di Paola M., Heuer R., Pirrotta A.: Fractional visco-elastic Euler–Bernoulli beam. Int. J. Solid Struct. 50, 3505-510 (2013)CrossRef
  6.Lei Y., Murmu T., Adhikari S., Friswell M.I.: Dynamic characteristics of damped viscoelastic nonlocal Euler–Bernoulli beam. Eur. J. Mech. A Solid 42, 125-36 (2013)MathSciNet CrossRef
  7.Chondros T.G., Dimarogonas A.D., Yao J.: A continuous cracked beam vibration theory. J. Sound Vib. 215, 17-4 (1998)MATH CrossRef
  8.Shifrin E.I., Routolo R.: Natural frequencies of a beam with an arbitrary number of cracks. J. Sound Vib. 222, 409-23 (1999)CrossRef
  9.Lee H.P., Ng T.Y.: Dynamic response of a cracked beam subject to a moving load. Acta Mech. 106, 221-30 (1994)MATH CrossRef
  10.Mahmoud M.A., Zaid M.A.: Dynamic response of a beam with a crack subject to a moving mass. J. Sound Vib. 256, 591-03 (2002)CrossRef
  11.Patil D.P., Maiti S.K.: Experimental verification of a method of detection of multiple cracks in beams based on frequency measurements. J. Sound Vib. 281, 439-51 (2005)CrossRef
  12.Nahvi H., Jabbari M.: Crack detection in beams using experimental modal data and finite element model. Int. J. Mech. Sci. 47, 1477-497 (2005)CrossRef
  13.Shafiei M., Khaji N.: Analytical solutions for free and forced vibrations of a multiple cracked Timoshenko beam subject to a concentrated moving load. Acta Mech. 221, 79-7 (2011)MATH CrossRef
  14.Lin H.P., Chang S.C.: Forced responses of cracked cantilever beams subjected to a concentrated moving load. Int. J. Mech. Sci. 48, 1456-463 (2006)MATH CrossRef
  15.Rieker J.R., Trethewey M.W.: Finite element analysis of an elastic beam structure subjected to a moving distributed mass train. Mech. Syst. Signal Process. 13, 31-1 (1999)CrossRef
  16.Doyle J.F.: Wave Propagation in Structures, 2nd edn. Springer, New York (1997)CrossRef
  17.Doyle J.F.: A spectrally formulated finite element for longitudinal wave propagation. Int. J. Anal. Exp. Modal Anal. 3, 1- (1988)MathSciNet
  18.Doyle J.F., Farris T.N.: A spectrally formulated finite element for flexural wave propagation in beams. Int. J. Anal. Exp. Modal Anal. 5, 13-3 (1990)
  19.Gopalakrishnan S., Martin M., Doyle J.F.: A matrix methodology for spectral analysis of wave propagation in multiple connected Timoshenko beams. J. Sound Vib. 158, 11-4 (1992)MATH CrossRef
  20.Hajheidari H., Mirdamadi H.R.: Frequency-dependent vibration analysis of symmetric cross-ply laminated plate of Levy-type by spectral element and finite strip procedures. Appl. Math. Model. 37, 7193-205 (2013)MathSciNet CrossRef
  21.Hajheidari H., Mirdamadi H.R.: Free and transient vibration analysis of an un-symmetric cross-ply laminated plate by spectral finite elements. Acta Mech. 223, 2477-492 (2012)MATH MathSciNet CrossRef
  22.Roy Mahapatra D., Gopalakrishnan S.: A spectral finite element model for analysis of axial–flexural–shear coupled wave propagation in laminated composite beams. Compos. Struct. 59, 67-8 (2003)CrossRef
  23.Vinod K.G., Gopalakrishnan S., Ganguli R.: Free vibration and wave propagation analysis of uniform and tapered rotating beams using spectrally formulated finite elements. Int. J. Solids Struct. 44, 5875-893 (2007)MATH CrossRef
  24.Lee U., Oh H.: Dynamics of an axially moving viscoelastic beam subject to axial tension. Int. J. Solids Struct. 42, 2381-398 (2005)CrossRef
  25.Azizi N., Saadatpour M.M., Mahzoon M.: Using spectral element method for analyzing continuous beams and bridges subjected to a moving load. Appl. Math. Model. 36, 3580-592 (2012)MATH MathSciNet CrossRef
  26.Lee U.: Spectral Element Method in Structural Dynamics. Wiley, Singapore (2009)MATH CrossRef
  27.Ariaei A., Ziaei-Rad S., Ghayour M.: Repair of a cracked Timoshenko beam subjected to a moving mass using piezoelectric patches. Int. J. Mech. Sci. 52, 1074-091 (2010)CrossRef
  28.Bathe K.J.: Finite Element Procedures. Prentice-Hall, Englewood Cliffs (1996)
  29.Ariaei A., Ziaei-Rad S., Ghayour M.: Vibration analysis of beams with open and breathing cracks subjected to moving masses. J. Sound Vib. 326, 709-24 (2009)CrossRef
  
• 作者单位：Vahid Sarvestan (1)
  Hamid Reza Mirdamadi (1)
  Mostafa Ghayour (1)
  Ali Mokhtari (1)
  
  1. Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, 84156-83111, Iran
  
• 刊物类别：Engineering
• 刊物主题：Theoretical and Applied Mechanics
  Mechanics, Fluids and Thermodynamics
  Continuum Mechanics and Mechanics of Materials
  Structural Mechanics
  Vibration, Dynamical Systems and Control
  Engineering Thermodynamics and Transport Phenomena
  
• 出版者：Springer Wien
• ISSN：1619-6937

文摘

In this article, a spectral finite element (SFE) model is presented for vibration analysis of a cracked viscoelastic beam subjected to moving loads. The dynamic shape functions are derived from the exact solution of the governing wave equations and are utilized for frequency-domain representation of a moving load. It is considered with either constant velocity or acceleration; then, the force vector for each spectral element is evaluated. The cracked beam is modeled as two segments connected by a massless rotational spring; thus, the beam dynamic stiffness matrix is extracted in frequency domain by considering compatibility conditions at the crack position. The effects of change in velocity and acceleration of moving load, crack parameters, and viscoelastic material properties on the dynamic response of the SFE beam model are investigated. The accuracy of SFE results is compared with that of finite elements. The results show the ascendency of the SFE model, as compared to FEM, for reducing the number of elements and computational effort, but increasing numerical accuracy.