Abstract
On the basis of Hamilton principle, the equation of solid-liquid coupling vibration of pipe conveying fluid is deduced. An asymmetrical solid-liquid coupling damp matrix and a symmetrical solid-liquid coupling stiffness matrix are obtained. UsingQR method, pipe's nature frequencies are calculated. The curves of the first four orders of natural frequency-flow velocity of pipe waw given. The influence of flowing velocity, pressure, solid-liquid coupling damp and solid-liquid coupling stiffness on natural frequency are discussed respectively. The dynamic respondence of the pipes for stepload with different flow velocity are calculated by Newmark method. It is found that, with the flow velocity increased, the nature frequency of the pipes reduced, increased, reduced again and so on.
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References
G. W. Housner, Bending vibration of a pipe line containing flowing fluid,J. Appl. Mech.,19, 6 (1952), 205–208.
V. Y.Feodosiev, The vibration and stability of pipe conveying fluid,Handbook of Engineers,10, 3 (1951). (in Russian)
R. H. Long, Experimental and theoretical study of Transverse vibration of a tube containing flowing fluid,J. Appl.,22, 6 (1955), 65–68.
R. W. Gregory and M. P. Paidoussis, Unstable oscillation of Tubular cantilevers conveying fluid—I Theory,Proc., Roy. Soc., London, Ser.A 293, 5 (1966), 512–527.
T. B. Benjamin, Dunamics of system of articulated pipes conveying fluid—II Experiments,Proc. Roy. Soc., London. Ser.A 261, 5 (1961), 457–499.
J. L. Hill and C. P. Swanson, Effects of lumped masses on the stability of fluid conveying tubes,J. Appl. Mech. 37, 4 (1970), 494–497.
A. K. Bajaj, Hopf bifurcation phenomena in pipes carrying fluid,J. Appl. Mech.,47, 5 (1980), 213–230.
J. Rousselet and G. erremann., Dynamics behavior of continuos cantilevered pipes conveying fluid near critical velocities,J. Appl. Mech.,48, (1981), 943–947.
M. P. Paidoussis, X. G. Li and R. H. Rand, Comparison between simulation, analysis and experiment of chaotic motion of a constrained pipe conveying fluid,J. Appl. Mech.,58, 4 (1991), 559–566.
X. D. Zhang, T. Du, etc., A correction for Housner's equation of pipe conveying fluid,Applied Mathematics and Mechanics (English Ed.),14, 2 (1993), 159–161.
Wang Benli and Wang Shizhong, Analyzing pipe solid liquid vibration by finite element method,Journal of Harbin Institute of Technology,16, 2 (1985), 8–14. (in Chinese)
Wang Shizhong and Wang Ru, The analysis of three dimension vibration of pipe conveying liquid,Journal of Harbin Institute of Technology,24, 4 (1992), 43–49 (in Chinese)
G. X. Li and M. P. Paidoussis, Stability double degeneracy and chaos in cantilevered pipes conveying fluid,International Journal of Nonlinear Mechanics,29, 1 (1994), 83–99.
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Shizhong, W., Yulan, L. & Wenhu, H. Research on solid-liquid coupling dynamics of pipe conveying fluid. Appl Math Mech 19, 1065–1071 (1998). https://doi.org/10.1007/BF02459195
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DOI: https://doi.org/10.1007/BF02459195