Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Vibration and stability of fluid conveying pipes with stochastic parameters

  • Ganesan, R. (Department of Mechanical Engineering, Concordia University) ;
  • Ramu, S. Anantha (Department of Civil Engineering, Indian Institute of Science)
  • Published : 1995.07.25
⟨ Previous Next ⟩

Abstract

Flexible cantilever pipes conveying fluids with high velocity are analysed for their dynamic response and stability behaviour. The Young's modulus and mass per unit length of the pipe material have a stochastic distribution. The stochastic fields, that model the fluctuations of Young's modulus and mass density are characterized through their respective means, variances and autocorrelation functions or their equivalent power spectral density functions. The stochastic non self-adjoint partial differential equation is solved for the moments of characteristic values, by treating the point fluctuations to be stochastic perturbations. The second-order statistics of vibration frequencies and mode shapes are obtained. The critical flow velocity is first evaluated using the averaged eigenvalue equation. Through the eigenvalue equation, the statistics of vibration frequencies are transformed to yield critical flow velocity statistics. Expressions for the bounds of eigenvalues are obtained, which in turn yield the corresponding bounds for critical flow velocities.

Keywords

References

  1. Anantha Ramu, S. and Ganesan, R. (1992), "Stability of stochastic Leipholz column with stochastic loadings", Arch. App. Mech., 62. pp. 363-375. https://doi.org/10.1007/BF00804597
  2. Anantha Ramu, S.and Ganesan, R. (1993), "A Galerkin finite element technique for stochastic field problems", Computer Methdos in Applied Mechanics and Engineering, 105, pp. 315-331. https://doi.org/10.1016/0045-7825(93)90061-2
  3. Anantha Ramu, S., Ganesan, R. and Sankar, T.S. (1992), "Stability analysis of nonconservatively loaded stochastic columns", Int. Jour. Solids and Structures, 29, pp. 2973-2988. https://doi.org/10.1016/0020-7683(92)90153-K
  4. Ariaratham, S.T. and Sri Namachchivaya, N. (1986), Dynamic stability of pipes conveying fluid with stochastic flow velocity in random vibration-status and recent developments, Eds.: Elishakoff, I. and Lyon, R.H., Elsevier, New York.
  5. Ariaratnam, S.T. and Sri Namachchivaya, N. (1986), "Dynamic stability of pipes conveying pulsating fluid", J. Sound Vib., 107, pp. 215-230. https://doi.org/10.1016/0022-460X(86)90233-6
  6. Ashley, H. and Haviland, G. (1950), Bending vibrations of a pipeline containing flowing fluid, J. App. Mech., 17 pp. 229- 232.
  7. Benjamin, T.B. (1961), "Dynamics of a system of articulated pipes conveying fluid I Theory", Proc. Roy. Soc. (London), A, 261, pp. 457-486. https://doi.org/10.1098/rspa.1961.0090
  8. Boyce, W.E. (1968), Random eigenvalue problems: in probabilistic methods in applied mathematics, Ed. Bhanucha-Reid. A.T., 1, Academic Press, New York. pp. 1-73.
  9. Chen, S.S. (1972), "Vibration and stability of a uniformly curved tube conveying fluid", J. Acous. Soc. America, 51, pp.223-232. https://doi.org/10.1121/1.1912834
  10. Collins, D. and Thomson, W.T. (1969)," The eigenvalue problem for structural systems with statistical properties", AIAA J., 7, pp. 642-648. https://doi.org/10.2514/3.5180
  11. Ganesan, R., Sankar, T.S. and Ramu, S.A. (1993), "Non conservatively loaded stochastic columns", Int. J. Solids and Structures, 30, pp. 2407-2424. https://doi.org/10.1016/0020-7683(93)90126-R
  12. Gregory, R.W. and Paidoussis, M.P. (1966), "Unstable oscillation of tubular cantilevers conveying fluid I theory", Proc. Roy. Soc. (London), A, 293, pp. 512-528. https://doi.org/10.1098/rspa.1966.0187
  13. Herrmann, G. (1971), Determinism and uncertainty in stability: in instability of continuous systems, IUTAM Symp., Herrenalb, 1969, Springer-Verlag, Berlin.
  14. Ibrahim, R.A. (1987), "Structural dynamics with parameter uncertainties", App. Mech. Rev., 40, pp. 309-328. https://doi.org/10.1115/1.3149532
  15. Kozin, F.(1988), Stability of flexible structures with random parameters: in stochastic structural dynamics, Eds.: Ariarantnam, S.T., Schueller, G.I. and Elishakoff, I. Elsevier, New York.
  16. Paidoussis, M.P. and Issid, N.T. (1974), "Dynamic stability of pipes conveying fluid", J. Sound Vib., 33, pp. 267-294. https://doi.org/10.1016/S0022-460X(74)80002-7
  17. Pauli Pedersen and Seyranian, A.P. (1983), "Sensitivity analysis for problems of dynamic stability", IJSS, 19, pp. 315-335.
  18. Plaut, R.H. and Infante, E.F. (1970), "On the stability of some continuous systems subjected to random excitations", J. App. Mech., 37, pp. 623-627. https://doi.org/10.1115/1.3408590
  19. Rajan, M., Nelson, H.D. and Chen, W.J. (1986), "Parameter sensitivities in the dynamics of rotor-bearing systems", J. Vib. Acous. Str. Rel. Dsn., Trans. ASME, 108, pp. 197-206. https://doi.org/10.1115/1.3269324
  20. Shinozuka, M. and Astill, C.A. (1972), "Random eigenvalue problems in structural analysis", AIAA J., 10, pp. 456-462. https://doi.org/10.2514/3.50119
  21. Shinozuka, M. and Lenoe, E. (1976), "A probabilistic model for spatial distribution of material properties", J. Eng. Frac. Mech., 8, pp. 217-227. https://doi.org/10.1016/0013-7944(76)90087-4
  22. Soong, T.T. and Cozzarelli, F.A. (1976), "Vibration of disordered structural systems", Shock Vib. Digest., 8, pp. 21-35.
  23. Vanmarcke, E. (1983), Random fields: analysis and synthesis, MIT Press, Cambridge.
  24. Vom Scheidt, J. and Purkert, W. (1983), Random eigenvalue problems, Elsevier Science Publishing Co., New York.

Cited by

  1. Reliability analysis of pipe conveying fluid with stochastic structural and fluid parameters vol.122, 2016, https://doi.org/10.1016/j.engstruct.2016.04.052
  2. Divergence instability of pipes conveying fluid with uncertain flow velocity vol.491, 2018, https://doi.org/10.1016/j.physa.2017.09.022
  3. Vibration analysis of silica nanoparticle-reinforced concrete pipes filled with compressible fluid surrounded by soil foundation 2018, https://doi.org/10.1002/suco.201700185
  4. Dynamic stability of a pipe conveying fluid with an uncertain computational model vol.49, 2014, https://doi.org/10.1016/j.jfluidstructs.2014.05.003
  5. Overview of Mechanics of Pipes Conveying Fluids—Part I: Fundamental Studies vol.132, pp.3, 2010, https://doi.org/10.1115/1.4001271
  6. Comparison of different cylindrical shell theories for stability of nanocomposite piezoelectric separators containing rotating fluid considering structural damping vol.23, pp.6, 1995, https://doi.org/10.12989/scs.2017.23.6.691
  7. Stochastic Finite-Element Modeling and Dynamic Characteristics Analysis of Pipe-Conveying Fluid vol.7, pp.3, 1995, https://doi.org/10.1007/s42417-019-00118-z