The equations of motion of curved pipes conveying fluid

Abstract The non-linear differential equations of motion of a fluid conveying pipe, the no-flow configuration of which is in the shape of a one-dimensional line arbitrarily curved and twisted in space, are derived by making use of the Newtonian approach. The extensible dynamics of the beam is based on the Timoshenko beam theory. Some significant differences with the equations available in the open literature are discussed. The stressed-by-flow configuration is found to be the only equilibrium state adequate for the study of the linear stability of such pipe-fluid systems.

[1]  David G. Jones,et al.  Vibration and Shock in Damped Mechanical Systems , 1968 .

[2]  Irving H. Shames.  Mechanics of Fluids , 1962 .

[3]  Charles W. Bert,et al.  A perturbation solution for non-linear vibration of uniformly curved pipes conveying fluid , 1986 .

[4]  James L. Hill,et al.  The Effect of Initial Forces on the Hydroelastic Vibration and Stability of Planar Curved Tubes , 1974 .

[5]  Shoei‐sheng Chen,et al.  Vibration and Stability of a Uniformly Curved Tube Conveying Fluid , 1972 .

[6]  B. E. Laithier,et al.  Dynamics of Timoshenko Beams Conveying Fluid , 1976 .

[7]  M. P. Païdoussis,et al.  On the dynamics of curved pipes transporting fluid. Part I: Inextensible theory , 1988 .

[8]  S. S. Chen.  Analysis of extensible curved pipes conveying fluid , 1975 .

[9]  Michael P. Païdoussis,et al.  Flow-induced Instabilities of Cylindrical Structures , 1987 .

[10]  W. H. Wittrick.  On elastic wave propagation in helical springs , 1966 .

[11]  C. D. Mote,et al.  On the Dynamic Analysis of Curved and Twisted Cylinders Transporting Fluids , 1976 .

[12]  W. Chen,et al.  Vibration and Stability of Helical Pipes Conveying Fluid , 1987 .

[13]  V. S. Deryabin,et al.  Oscillations of a conduit of constant curvature , 1975 .

[14]  M. Païdoussis,et al.  Dynamic stability of pipes conveying fluid , 1974 .

[15]  Shoei‐sheng Chen,et al.  Out-of-Plane Vibration and Stability of Curved Tubes Conveying Fluid , 1973 .

[16]  G. Cowper.  The Shear Coefficient in Timoshenko’s Beam Theory , 1966 .

[17]  M. Païdoussis,et al.  Unstable oscillation of tubular cantilevers conveying fluid I. Theory , 1966, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[18]  A. Love.  A treatise on the mathematical theory of elasticity , 1892 .

[19]  S. S. Chen.  FLOW-INDUCED IN-PLANE INSTABILITIES OF CURVED PIPES. , 1972 .

[20]  C. Dupuis,et al.  Application of the transfer matrix method to non-conservative systems involving fluid flow in curved pipes , 1985 .

[21]  M. P. Païdoussis,et al.  The equations of motion of initially stressed Timoshenko tubular beams conveying fluid , 1981 .

[22]  G. Steven Gipson,et al.  Instability of Internally Damped Curved Pipes , 1990 .

[23]  T. E. Unny,et al.  Hydroelastic Instability of Uniformly Curved Pipe-Fluid Systems , 1970 .

[24]  V. A. Svetlitsky.  Vibration of tubes conveying fluids , 1977 .

[25]  C. A. Desoer,et al.  Nonlinear Systems Analysis , 1978 .

[26]  On the motion of a curved and twisted rod , 1972 .

[27]  E. Reissner.  On one-dimensional finite-strain beam theory: The plane problem , 1972 .

[28]  Stephen P. Timoshenko,et al.  Vibration problems in engineering , 1928 .

[29]  Thomas Brooke Benjamin,et al.  Dynamics of a system of articulated pipes conveying fluid - II. Experiments , 1961, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.