Stability of a Cluster of Flexible Cylinders in Bounded Axial Flow

1977 ◽  
Vol 44 (3) ◽  
pp. 401-408 ◽  
Author(s):  
M. P. Paidoussis ◽  
S. Suss
Keyword(s):  
Channel Wall ◽  
Cylindrical Channel ◽  
Equations Of Motion ◽  
Axial Flow ◽  
High Flow ◽  
Critical Flow ◽  
Flowing Fluid ◽  
Hydrodynamic Coupling ◽  
Viscous Hydrodynamic ◽  
Flow Velocities

This paper deals with the dynamics of a cluster of parallel flexible cylinders in a cylindrical channel in the presence of an axially flowing fluid. The equations of motion are derived, taking into account inviscid and viscous hydrodynamic coupling of small arbitrary motions of the cylinders. Solutions of the equations of motion yield the eigenfrequencies and modal shapes of the system. For sufficiently high flow velocities the system loses stability by divergence and flutter, similarly to a solitary cylinder in unbounded flow; however, the critical flow velocities are much lower, as proximity to other cylinders and to the channel wall severely destabilize the system.

Experiments on Fluidelastic Instability of Cylinder Clusters in Axial Flow

1982 ◽  
Vol 104 (3) ◽  
pp. 342-347 ◽  
Author(s):  
M. P. Paidoussis ◽  
LI. R. Curling ◽  
J. O. Gagnon
Keyword(s):  
Natural Frequencies ◽  
Axial Flow ◽  
High Flow ◽  
Strain Gauges ◽  
Critical Flow ◽  
Water Tunnel ◽  
Random Vibrations ◽  
General Behavior ◽  
Good Agreement ◽  
Flow Velocities

This paper presents a summary of the general behavior of cylinder clusters in axial flow and especially of the fluidelastic instabilities which occur at high flow velocities. Experiments were conducted in a water tunnel with three- and four-cylinder clusters, and the behavior was monitored either optically or by instrumenting one of the cylinders with strain gauges. With increasing flow, the amplitude of small random vibrations of the cylinders increased; simultaneously, the natural frequencies, as a group, decreased, which is in good agreement with theory. The cylinders eventually lost stability by buckling (divergence), and at higher flow by flutter. Agreement between theoretical and experimental critical flow velocities for these fluidelastic instabilities has been found to be good.

Paper 15: Vibration of Flexible Cylinders with Supported Ends, Induced by Axial Flow

1965 ◽  
Vol 180 (10) ◽  
pp. 268-279
Author(s):  
M. P. Paidoussis
Keyword(s):  
Cross Flow ◽  
Axial Flow ◽  
High Flow ◽  
Flexible Cylinder ◽  
Empirical Expression ◽  
Flexible Material ◽  
Amplitude Vibration ◽  
Critical Velocities ◽  
Flow Components ◽  
Flow Velocities

A flexible cylinder with pinned ends in axial flow of sufficiently high flow velocity is subject to buckling and oscillatory hydroelastic instabilities. These instabilities are discussed briefly and it is shown that they occur at such high flow velocities that they are not likely to be encountered in practice, unless the cylinder is made of very flexible material such as rubber. The cylinder is subjected to small amplitude vibration, however, even at flow velocities very much smaller than the critical velocities for hydroelastic instabilities. The mechanism of energy transfer from the fluid to the cylinder is examined and it is postulated that this vibration is excited by cross-flow components of flow and other departures from steady, uniform and perfectly axial flow. Experimental evidence supporting this postulate is presented. An empirical expression is given for the amplitude of vibration based on reported experimental observations covering a variety of geometries, fluids and cylinder materials.

Experiments on vertical slender flexible cylinders clamped at both ends and subjected to axial flow

2007 ◽  
Vol 366 (1868) ◽  
pp. 1275-1296 ◽  
Author(s):  
Y Modarres-Sadeghi ◽  
M.P Païdoussis ◽  
C Semler ◽  
E Grinevich
Keyword(s):  
Axial Flow ◽  
Quantitative Agreement ◽  
Dynamical Behaviour ◽  
High Flow ◽  
The Third ◽  
Theoretical Predictions ◽  
Series Of Experiments ◽  
Linear And Nonlinear ◽  
Theory And Experiment ◽  
Flow Velocities

Three series of experiments were conducted on vertical clamped–clamped cylinders in order to observe experimentally the dynamical behaviour of the system, and the results are compared with theoretical predictions. In the first series of experiments, the downstream end of the clamped–clamped cylinder was free to slide axially, while in the second, the downstream end was fixed; the influence of externally applied axial compression was also studied in this series of experiments. The third series of experiments was similar to the second, except that a considerably more slender, hollow cylinder was used. In these experiments, the cylinder lost stability by divergence at a sufficiently high flow velocity and the amplitude of buckling increased thereafter. At higher flow velocities, the cylinder lost stability by flutter (attainable only in the third series of experiments), confirming experimentally the existence of a post-divergence oscillatory instability, which was previously predicted by both linear and nonlinear theory. Good quantitative agreement is obtained between theory and experiment for the amplitude of buckling, and for the critical flow velocities.

Dynamics of Slender Tapered Beams With Internal or External Axial Flow—Part 1: Theory

1979 ◽  
Vol 46 (1) ◽  
pp. 45-51 ◽  
Author(s):  
M. J. Hannoyer ◽  
M. P. Paidoussis
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Thickness ◽  
Equations Of Motion ◽  
Axial Flow ◽  
Internal Flow ◽  
External Flow ◽  
High Flow ◽  
Flow Passage ◽  
Flow Part ◽  
Surrounding Fluid

This paper develops a general theory for the dynamics of slender, nonuniform axisymmetric beams subjected to either internal or external flow, or to both simultaneously. The effect of the boundary layer of the external flow is taken into account in the formulation. Typical solutions of the equations of motion are presented for cantilevered conical beams in external flow and for beams with a conical internal flow passage. Such systems lose stability at sufficiently high flow velocity, internal or external, either by flutter or by buckling. The effect of several parameters is investigated. For internal flow, the internal and external shape, whether uniform or conical, and the density of the surrounding fluid have sometimes unexpected effects on stability; e.g., tubular beams lose stability at lower internal flow when immersed in water than when in air. For external flow the effects of conicity, free end shape and boundary-layer thickness are investigated; the latter has a strong stabilizing influence, such that simple theory neglecting this effect results in serious error.

scholarly journals Dynamics and Stability of a Flexible, Slender Cylinder Flexibly Restrained at One End and Free at the Other and Subjected to Axial Flow

2016 ◽  
Vol 63 (3) ◽  
pp. 379-396 ◽  
Author(s):  
Mojtaba Kheiri
Keyword(s):  
Ritz Method ◽  
Axial Flow ◽  
Equation Of Motion ◽  
The Other ◽  
Critical Flow ◽  
Rotational Spring ◽  
Lagrange’S Equations ◽  
Translational Spring ◽  
Lagrange's Equations ◽  
Flow Velocities

Abstract In this paper, Lagrange’s equations along with the Ritz method are used to obtain the equation of motion for a flexible, slender cylinder subjected to axial flow. The cylinder is supported only by a translational and a rotational spring at the upstream end, and at the free end, it is terminated by a tapering end-piece. The equation of motion is solved numerically for a system in which the translational spring is infinitely stiff, thus acting as a pin, while the stiffness of the rotational spring is generally non-zero. The dynamics of such a system with the rotational spring of an average stiffness is described briefly. Moreover, the effects of the length of the cylinder and the shape of the end-piece on the critical flow velocities and the modal shapes of the unstable modes are investigated.

Bifurcations in Three-Dimensional Motions of Articulated Tubes, Part 2: Nonlinear Analysis

1982 ◽  
Vol 49 (3) ◽  
pp. 612-618 ◽  
Author(s):  
A. K. Bajaj ◽  
P. R. Sethna
Keyword(s):  
Nonlinear Analysis ◽  
Periodic Solutions ◽  
Flow Parameter ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Critical Flow ◽  
Tube System ◽  
Flow Velocities

The equations of motion of the two-segment articulated tube system, discussed in Part 1, are analyzed for bifurcating periodic solutions near critical flow velocities. In addition to the flow parameter, the system depends on four other parameters. Depending on the values of these parameters the system exhibits a wide variety of behavior. This behavior is studied in detail in several specific cases.

Vibration and Stability of Helical Pipes Conveying Fluid

1987 ◽  
Vol 109 (4) ◽  
pp. 402-410 ◽  
Author(s):  
C.-N. Fan ◽  
W.-H. Chen
Keyword(s):  
Natural Frequencies ◽  
Equations Of Motion ◽  
Mode Shapes ◽  
Critical Flow ◽  
Helical Pipe ◽  
End Conditions ◽  
Finite Element Procedure ◽  
Pipes Conveying Fluid ◽  
Conveying Fluid ◽  
Flow Velocities

This paper presents an accurate finite element procedure for the vibration and stability analysis of helical pipe conveying fluid. The kinematics of the helical pipe are derived including the effects of arbitrary curvatures and torsions in a nonorthogonal helical coordinate system. The equations of motion are derived from the Hamilton’s principle for mass transport system and the shear deformation and rotary inertia are also considered. The 3-node space-curved isoparametric element is used. The natural frequencies, mode shapes and critical flow velocities of buckling are studied for different end conditions. The significant influence of torsion effects on the calculation of natural frequencies and critical flow velocities is found. To demonstrate the validity and accuracy of the techniques developed, several numerical examples are illustrated.

scholarly journals The Debris Content of Surging Glaciers in Svalbard and Iceland

1975 ◽  
Vol 14 (72) ◽  
pp. 395-406 ◽  
Author(s):  
Chalmers M. Clapperton
Keyword(s):  
Bottom Sediments ◽  
High Flow ◽  
Frictional Heat ◽  
Horizontal Extent ◽  
Compressive Flow ◽  
Melt Water ◽  
Terminal Zone ◽  
Trigger Zone ◽  
Vertical Development ◽  
Flow Velocities

In Svalbard and Iceland there appears to be much more debris entrained in glaciers that surge than in those which do not. Conditions particularly favourable for the basal incorporation of debris develop as a consequence of the high flow velocities attained by a surge. These are increased cavitation in the lee of obstacles and an increased supply of basal melt water resulting from frictional heat and from the trigger zone. Layers of regelation ice incorporating debris can thus develop to a much greater vertical and horizontal extent than in non-surging glaciers. Excessive shearing, and the distortion of foliation structures in the terminal zone of compressive flow, enhance the vertical development of the debris-rich regelation layers. Glaciers that surge over outwash and/or fjord-bottom sediments become particularly rich in debris.

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