TECHNICAL PAPERS
Jan 1, 1990

Instability of Internally Damped Curved Pipes

Publication: Journal of Engineering Mechanics
Volume 116, Issue 1

Abstract

The equation of motion of a fulid‐conveying pipe that includes the effect of damping is derived on the basis of Hamilton's principle. Depending upon the constraint conditions on the ends of the pipe, the induced or applied end forces may be classified as being either conservative or nonconservative. It is shown that when internal damping is taken into consideration, the conservative system could be subjected to a flutter type of instability. In certain cases, the capacity of the curved pipe to sustain flow is greatly affected by the internal damping factor. Under increasing fluid velocity, the pipes with an angle of bend less than 90° yield natural frquencies that do not follow the pattern of the pipe bends with angles of bend greater than 90°. Numerical results are presented for a wide range of parameters, including fluid velocity, damping parameter, and angle of the pipe bend.

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References

1.
Ashley, H., and Haviland, G. (1950). “Bending vibration of a pipeline containing flowing fluid.” Trans., J. Appl. Mech., ASME, 17, 229–232.
2.
Benjamin, T. B. (1961a). “Dynamics of a system of articulated pipes conveying fluid: I, theory.” Proc. Royal Soc., A, 261, 457–486.
3.
Benjamin, T. B. (1961b). “Dynamics of a system of articulated pipes conveying fluid: II, experiments.” Proc. Royal Soc., A, 261, 487–499.
4.
Chen, S. S. (1972). “Vibration and stability of a uniformly curved tube conveying fluid.” J. Acoustical Soc. of America, 51(2), 223–232.
5.
Chen, S. S. (1973). “Flow induced inplane stability of curved pipes.” Nuclear Engrg. and Design, 23, 29–38.
6.
Chen, S. S. (1977). “Flow induced vibrations of circular cylindrical structures. I: stationary fluid flow and parallel flow.” The Shock and Vibration Digest, 9, 25–38.
7.
Doli, R. W., and Mote, C. D. (1976). “On the dynamic analysis of curved and twisted cylinders transporting fluids.” J. Pressure Vessel Tech., 98, 143–150.
8.
Gregory, R. W., and Paidousis, M. P. (1966a). “Unstable oscillation of tubular cantilevers conveying fluid: I, theory.” Proc. Royal Society, A, 293, 512–517.
9.
Gregory, R. W. and Paidousis, M. P. (1966b). “Unstable oscillation of tubular cantilevers conveying fluid: II, experiments.” Proc. Royal Soc., A, 293, 528–542.
10.
Herrmann, G., and Jong, I. C. (1965). “On nonconservative stability problems of elastic systems with slight damping.” J. Appl. Mech., 32, 1965, 125–133.
11.
Herrmann, G., and Nemat‐Nasser, S. (1967). “Energy considerations in the analysis of stability of nonconservative structural systems.” Stability of structures, G. Herrmann, ed., Pergamon Press, New York, N.Y.
12.
Hill, J. L., and Davis, C. G. (1974). “The effect of initial forces on the hydroelastic vibration and stability of planar curved tubes.” J. Appl. Mech., 41, 355–359.
13.
Holmes, P. J. (1978). “Pipes supported at both ends cannot flutter.” J. Appl. Mech., 45, 619–622.
14.
Housner, G. W. (1952). “Bending vibration of a pipeline containing flowing fluid.” J. Appl. Mech., ASME, 18, 205–208.
15.
Kohli, A. K., and Nakra, B. C. (1984). “Vibration analysis of straight and curved tubes conveying fluids by means of straight beam finite elements.” J. Sound and Vibration, 93, 307–311.
16.
Leipholz, H. (1968). “Uber das Verfahren von Grammelmit benachbarter Greenscher Funktion und die entsprechende Verallgemeinerung des Verfahrens von Galerkin.” Ingenieur‐Archiv, 37, 251–266.
17.
Leipholz, H. (1970). “Application of a generalized principle of Hamilton to nonconservative problems.” University of Waterloo report no. 38, Waterloo, Ontario.
18.
Leipholz, H. (1975). Direct variational methods and eigenvalue problems in engineering. Leyden Noordhoff Intl. Publishing.
19.
Naguleswaran, S., and Williams, C. J. (1968). “Lateral vibration of a pipe conveying a fluid.” J. Mech. Engrg. Sci., 10(3), 228–238.
20.
Nelms, H. A., and Segaser, C. L. (1969). Survey of nuclear reactor system primary circuit heat exchangers. ORNAL 4399, Apr.
21.
Nemat‐Nasser, S. (1967). “On the stability of equilibrium of nonconservative continuous systems with slight damping.” J. Appl. Mech., 34, 344–397.
22.
Nemat‐Nasser, S., and Herrmann, G. (1966b). “Some general considerations concerning the destabilizing effect in nonconservative systems.” Z. Angew. Math. Phys., 17, 303–401.
23.
Nemat‐Nasser, S., Prasad, S. N., and Herrmann, G. (1966). “Destabilising effect of velocity dependent forces in nonconservative continuous systems.” AIAA J., 4(7), 1276–1280.
24.
Paidoussis, M. P., and Issid, N. T. (1974). “Dynamic stability of pipes conveying fluids.” J. Sound and Vibration, 33, 267–294.
25.
Paidoussis, M. P. (1975). “Flutter of a conservative system of pipes conveying incompressible fluid.” J. Mech. Engrg. Sci., 17, 19–25.
26.
Roth, V. N. (1964). “Instabilitat durchstromter Rohre.” Ingenieur Archiv, 33(4), 236–263.
27.
Shieh, R. (1968). “Variational method in the stability analysis of nonconservative problems.” Zeitschrift fur angewandte Mathematik und Physik, 19, 88–100.
28.
Stein, R. A., and Torbriner, M. W. (1970). “Vibration of pipes containing flowing fluid.” J. Appl. Mech., ASME, 92, 906–916.
29.
Unny, T. E., Martin, E. L., and Duby, R. N. (1970). “Hydroelastic instability of uniformly curved pipes.” Trans., J. Appl. Mech., ASME, 817–822.
30.
Wambsganss, V. W., Jr. (1967). “Vibration of reactor core components, reactorfuel process.” Technology, 10, Summer, 208.
31.
Zeigler, H. (1968). Principles of structural stability, Blaisdell Publishing Co., Waltham, Mass.

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Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 116Issue 1January 1990
Pages: 77 - 90

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Published online: Jan 1, 1990
Published in print: Jan 1990

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R. Aithal
Res. Asst., School of Civ. Engrg., Oklahoma State Univ., Stillwater, OK 74078
G. Steven Gipson
Assoc. Prof., School of Civ. Engrg., Oklahoma State Univ., Stillwater, OK

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