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Vibration Analysis for the In-plane Motions of a Semi-Circular Pipe Conveying Fluid Considering the Geometric Nonlinearity

기하학적 비선형성을 고려한 유체를 수송하는 반원관의 면내운동에 대한 진동 해석

  • 정진태 (한양대학교 기계정보경영공학부) ;
  • 정두한 (한양대학교 정밀기계공학과)
  • Published : 2004.12.01

Abstract

The vibration of a semi-circular pipe conveying fluid is studied when the pipe is clamped at both ends. To consider the geometric nonlinearity, this study adopts the Lagrange strain theory for large deformation and the extensible dynamics based on the Euler-Bernoulli beam theory for slenderness assumption. By using the Hamilton principle, the non-linear partial differential equations are derived for the in-plane motions of the pipe, considering the fluid inertia forces as a kind of non-conservative forces. The linear and non-linear terms in the governing equations are compared with those in the previous study, and some significant differences are discussed. To investigate the dynamic characteristics of the system, the discretized equations of motion are derived from the Galerkin method. The natural frequencies varying with the flow velocity are computed from the two cases, which one is the linear problem and the other is the linearized problem in the neighborhood of the equilibrium position. Finally, the time responses at various flow velocities are directly computed by using the generalized-$\alpha$ method. From these results, we should consider the geometric nonlinearity to analyze dynamics of a semi-circular pipe conveying fluid more precisely.

Keywords

In-Plane Motion;Semi-Circular Pipe;Pipe Conveying Fluid;Geometric Nonlinearity

References

  1. Paidoussis, M.P., 1998, Fluid-Structure Interactions, Volume I: Slender Structure and Axial Flow, Academic Press
  2. Svetlisky, V.A., 1977, 'Vibration of Tubes Conveying Fluid,' Journal of Acoustical Society of America, Vol. 62, pp. 595-600 https://doi.org/10.1121/1.381560
  3. Chen, S.S., 1972, 'Vibration and Stability of a Uniformly Curved Tube Conveying Fluid,' Journal of Acoustical Society of America, Vol. 51, pp. 223-232 https://doi.org/10.1121/1.1912834
  4. Chen, S.S., 1973, 'Out-of-Plane Vibration and Stability of Curved Tubes Conveying Fluid,' Journal of Applied Mechanics, Vol. 40, pp. 362-368 https://doi.org/10.1115/1.3422988
  5. Hill, J.L. and Davis, C.G., 1974, 'The Effect of Initial Forces on the Hydrostatic Vibration and Stability of Planar Curved tubes,' Journal of Applied Mechanics, Vol. 41, pp. 355-359 https://doi.org/10.1115/1.3423292
  6. Misra, A.K., Paidoussis, M.P. and Van, K.S., 1988, 'On the Dynamics of Curved Pipes Transporting Fluid. Part I: Inextensible Theory,' Journal of Fluid and Structures, Vol. 2, pp. 211-244
  7. Misra, A.K., Paidoussis, M.P. and Van, K.S., 1988, 'On the Dynamics of Curved Pipes Transporting Fluid. Part II: Extensible Theory,' Journal of Fluid and Structures, Vol. 2, pp. 245-261 https://doi.org/10.1016/S0889-9746(88)80010-0
  8. Dupuis, C. and Rousselet, J., 1992, 'The Equations of Motion of Fluid Conveying Curved Pipes,' Journal of Sound and Vibration, Vol. 153, pp. 473-489 https://doi.org/10.1016/0022-460X(92)90377-A
  9. Dupuis, C. and Rousselet, J., 1993, 'Hamilton's Principle and the Governing Equations of Motion of Fluid Conveying Curved Pipes,' Journal of Sound and Vibration, Vol. 160, pp. 172-174 https://doi.org/10.1006/jsvi.1993.1013
  10. Pak, C.H., Hong, S.C. and Kim, T.J., 1997, 'Chaotic Vibration of a Curved Pipe Conveying Oscillatory Flow,' Trans. of KSNVE, Vol. 7, No.3, pp.489-498
  11. Lee, S.I. and Chung, J., 2002, 'Nonlinear Vibration Characteristics of a Curved Pipe with Fixed Ends and Steady Internal Flow,' Trans. of KSME (A), Vol. 26, No. 1, pp. 61-66 https://doi.org/10.3795/KSME-A.2002.26.1.061
  12. Lee, S.I. and Chung, J., 2002, 'New Non-Linear Modelling for Vibration Analysis of a Straight Pipe Conveying Fluid,' Journal of Sound and Vibration, Vol. 254, No.2, pp. 313-325 https://doi.org/10.1006/jsvi.2001.4097
  13. Blevins, R.D., 1979, Formulas for Natural Frequency and Mode Shape, Van Nostrand Reinhold
  14. Love, A.E.H., 1927, A Treatise on the Mathematical Theory of Elasticity, Cambridge University Press