Journal of Mechanical Science and Technology

, Volume 27, Issue 9, pp 2637–2643 | Cite as

Eulerian and lagrangian descriptions for the vibration analysis of a deploying beam

Article
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Abstract

In this study, the equations of motion derived from the Eulerian and Lagrangian descriptions of the vibration analysis of a deploying beam are compared and discussed. After transforming the equations to their corresponding variational equations, the discretized equations for the two descriptions are derived and their equivalence is verified. The numerical time responses obtained from the equations of both descriptions are the same. We recommend use of the Lagrangian description over the Eulerian one when analyzing the vibration of a deploying beam that includes the entirety of the beam inside and outside a rigid wall.

Keywords

Eulerian description Lagrangian description Deploying beam Longitudinal and transverse vibrations 
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References

  1. [1]
    P. K. C. Wang and J. D. Wei, Vibrations in a moving flexible robot arm, Journal of Sound and Vibration, 116(1) (1987) 149–160.CrossRefGoogle Scholar
  2. [2]
    J. Yuh and T. Young, Dynamic modeling of an axially moving beam in rotation: simulation and experiment, Journal of Dynamic Systems, Measurement and, Control, Transactions of the ASME, 113(1) (1991) 34–40.CrossRefGoogle Scholar
  3. [3]
    M. Stylianou and B. Tabarrok, Finite element analysis of an axially moving beam, part I: time integration, Journal of Sound and Vibration, 178(4) (1994) 433–453.CrossRefGoogle Scholar
  4. [4]
    M. Stylianou and B. Tabarrok, Finite element analysis of an axially moving beam, part II: stability analysis, Journal of Sound and Vibration, 178(4) (1994) 455–481.CrossRefGoogle Scholar
  5. [5]
    B. O. Al-Bedoor and Y. A. Khulief, Finite element dynamic modeling of a translating and rotating flexible link, Computer Methods in Applied Mechanics and Engineering, 131(1–2) (1996) 173–189.CrossRefMATHGoogle Scholar
  6. [6]
    B. O. Al-Bedoor and Y. A. Khulief, Vibrational motion of an elastic beam with prismatic and revolute joints, Journal of Sound and Vibration, 190(2) (1996) 195–206.CrossRefGoogle Scholar
  7. [7]
    B. O. Al-Bedoor and Y. A. Khulief, An approximate analytical solution of beam vibrations during axial motion, Journal of Sound and Vibration, 192(1) (1996) 159–171.CrossRefGoogle Scholar
  8. [8]
    K. Behdinan, M. Stylianou and B. Tabarrok, Dynamics of flexible sliding beams non-linear analysis part I: formulation, Journal of Sound and Vibration, 208(4) (1997) 517–539.CrossRefGoogle Scholar
  9. [9]
    B. O. Al-Bedoor and Y. A. Khulief, General planar dynamics of a sliding flexible link, Journal of Sound and Vibration, 206(5) (1997) 641–661.CrossRefGoogle Scholar
  10. [10]
    R. F. Fung, P. Y. Lu and C. C. Tseng, Non-linearly dynamic modelling of an axially moving beam with a tip mass, Journal of Sound and Vibration, 218(4) (1998) 559–571.CrossRefGoogle Scholar
  11. [11]
    F. Gosselin, M. P. Paidoussis and A. K. Misra, Stability of a deploying/extruding beam in dense fluid, Journal of Sound and Vibration, 299(1–2) (2007) 123–142.CrossRefGoogle Scholar
  12. [12]
    W. Lin and N. Qiao, Vibration and stability of an axially moving beam immersed in fluid, International Journal of Solids and Structures, 45(5) (2008) 1445–1457.CrossRefMATHGoogle Scholar
  13. [13]
    M. T. Piovan and R. Sampaio, Vibrations of axially moving flexible beam made of functionally graded materials, Thin-Walled Structures, 46(2) (2008) 112–121.CrossRefGoogle Scholar
  14. [14]
    J. R. Chang, W. J. Lin, C. J. Huang and S. T. Choi, Vibration and stability of an axially moving Rayleigh beam, Applied Mathematical Modelling, 34(6) (2010) 1482–1497.MathSciNetCrossRefMATHGoogle Scholar
  15. [15]
    S. Park, H. H. Yoo and J. Chung, Longitudinal and transverse vibrations of an axially moving beam with deployment or retraction, AIAA Journal, 51(3) (2013) 686–696.CrossRefGoogle Scholar
  16. [16]
    J. Chung and G. M. Hulbert, A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-alpha method, Journal of Applied Mechanics, Transactions of the ASME, 60(2) (1993) 371–375.MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© The Korean Society of Mechanical Engineers and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringHanyang UniversityAnsanKorea
  2. 2.School of Mechanical EngineeringHanyang UniversitySeoulKorea

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