Dynamics of cantilevered pipes conveying fluid. Part 1: Nonlinear equations of three-dimensional motion

In a three-part study, the first part being this paper, the investigation of the three-dimensional nonlinear dynamics of unrestrained and restrained cantilevered pipes conveying fluid is undertaken. The full derivation of the equations of motion in three dimensions for the plain cantilevered pipe is presented first in this paper, using a modified version of Hamilton's principle, adapted for an open system. Intermediate (between the clamped and free end) nonlinear spring constraints are then incorporated into the equations of motion via the method of virtual work. Furthermore, a point mass fixed at the free end of the pipe is also added to the system. The equations of motion are presented in dimensionless form and then discretized with Galerkin's method.

[1]  Michael P. Païdoussis,et al.  Dynamics of cantilevered pipes conveying fluid. Part 2: Dynamics of the system with intermediate spring support , 2007 .

[2]  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.

[3]  M. P. Païdoussis,et al.  Nonlinear Dynamics of a Fluid-Conveying Cantilevered Pipe with an Intermediate Spring Support , 1993 .

[4]  Anil K. Bajaj,et al.  Flow induced bifurcations to three-dimensional oscillatory motions in continuous tubes , 1984 .

[5]  T. P. Luu,et al.  Dynamics of a pipe aspirating fluid such as might be used in ocean mining , 1985 .

[6]  Michael P. Païdoussis,et al.  Pipes Conveying Fluid: A Model Dynamical Problem , 1993 .

[7]  Anil K. Bajaj,et al.  Stability boundaries for flow induced motions of tubes with an inclined terminal nozzle , 1979 .

[8]  Yahya Modarres-Sadeghi,et al.  Dynamics of cantilevered pipes conveying fluid. Part 3: Three-dimensional dynamics in the presence of an end-mass , 2007 .

[9]  G. X. Li,et al.  The Non-linear Equations of Motion of Pipes Conveying Fluid , 1994 .

[10]  Cheng-Tien Chieu.  Bending vibrations of a pipe line containing flowing fluid , 1970 .

[11]  M. P. Paidoussis,et al.  Unstable oscillation of tubular cantilevers conveying fluid II. Experiments , 1966, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[12]  H. Troger,et al.  Heteroclinic cycles in the three-dimensional postbifurcation motion of O(2)-symmetric fluid conveying tubes , 1996 .

[13]  G. S. Copeland,et al.  Chaotic flow-induced vibration of a flexible tube with end mass , 1992 .

[14]  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.

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

[16]  Michael P. Païdoussis,et al.  Non-linear dynamics of a fluid-conveying cantilevered pipe with a small mass attached at the free end , 1998 .

[17]  M. P. Païdoussis,et al.  NUMERICAL SOLUTIONS OF SECOND ORDER IMPLICIT NON-LINEAR ORDINARY DIFFERENTIAL EQUATIONS , 1996 .

[18]  H. Troger,et al.  Nonlinear three-dimensional oscillations of elastically constrained fluid conveying viscoelastic tubes with perfect and broken O(2)-symmetry , 1995 .

[19]  Michael P. Païdoussis,et al.  1992 CALVIN RICE LECTURE: Some Curiosity-Driven Research in Fluid Structure Interactions and Its Current Applications , 1993 .