In this paper, the destabilization due to small damping of the follower force system, known as Beck’s problem, and of the cantilevered pipe conveying fluid system, two nonconservative systems, is considered. Instead of looking for a mathematical explanation, e.g., the evolution of the eigenvalues with different parameters, a more “physical” explanation is provided. It is shown that it is of particular interest to focus on the different modes of vibration and to understand how they evolve when damping is varied. Also, based on energy considerations, the key factors influencing stability are highlighted, e.g., the phase angles between the different coordinates. In the case of the pipe conveying fluid, the methodology developed and insight gained help explain the presence of “jumps” p in the stability curves, that are known to play an important role in the linear and nonlinear dynamics of this system.

1.
Benjamin
T. B.
,
1961
, “
Dynamics of a System of Articulated Pipes Conveying Fluid. I. Theory. II. Experiments
,”
Proceedings of the Royal Society, London
, Vol.
A261
, pp.
457
499
.
2.
Benjamin
T. B.
,
1963
, “
The Three-fold Classification of Unstable Disturbances in Flexible Surfaces Bounding lnviscid Flows
,”
Journal of Fluid Mechanics
, Vol.
16
, pp.
436
450
.
3.
Bolotin
V. V.
, and
Zhinzher
N. I.
,
1969
, “
Effects of Damping on Stability of Elastic Systems Subjected to Non-conservative Forces
,”
International Journal of Solids and Structures
, Vol.
5
, pp.
965
989
.
4.
Craik, A. D. D., 1985, Wave Interaction and Fluid Flows, Cambridge University Press, Cambridge, UK.
5.
Crandall
S. H.
,
1995
, “
The effect of Damping on the Stability of Gyroscopic Pendulums
,”
Zeitschrift fu¨r angewandte Mathematik und Physik
, Vol.
46
, special issue, pp.
S762–S780
S762–S780
.
6.
Done, G. T. S., 1963, “The Effect of Linear Damping on Flutter Speed,” Aeronautical Research Council R&M, No. 3396.
7.
Drazin, P. G., and Reid, W. H., 1981, Hydrodynamic Stability, Cambrige University Press, Cambridge, UK.
8.
Gregory
R. W.
, and
Pai¨doussis
M. P.
,
1966
, “
Unstable Oscillation of Tubular Cantilevers Conveying Fluid. I. Theory; II. Experiments
,”
Proceedings of the Royal Society, London
, Vol.
293
, pp.
512
542
.
9.
Nemat-Nasser
S.
,
Prasad
S. N.
, and
Herrmann
G.
,
1966
, “
Destabilizing Effect of Velocity-dependent Forces in Non-conservative Continuous Systems
,”
AIAA Journal
, Vol.
4
, pp.
1276
1280
.
10.
Nissim
E.
,
1965
, “
Effect of Linear Damping on Flutter Speed. Part I: Binary Systems
,”
The Aeronautical Quaterly
, Vol.
16
, pp.
159
178
.
11.
Pai¨doussis
M. P.
,
1970
, “
Dynamics of Tubular Cantilevers Conveying Fluid
,”
I. Mech. E. Journal of Mechanical Engineering Science
, Vol.
12
, pp.
85
103
.
12.
Pai¨doussis, M. P., 1996, “Fluid-Structure Interactions between Axial Flows and Slender Structures,” Sectional Lecture, XIXth ICTAM, Kyoto, Japan.
13.
Pai¨doussis, M. P., 1998, Fluid-Structure Interactions: Slender Structures and Axial Flow, Vol. I, Academic Press, London.
14.
Pai¨doussis
M. P.
, and
Li
G. X.
,
1993
, “
Pipes Conveying Fluid: A Model Dynamical Problem
,”
Journal of Fluids and Structures
, Vol.
7
, pp.
137
204
.
15.
Pai¨doussis, M. P., Semler, C, and Alighanbari, H., 1997, “A Physical Explanation of the Destabilizing Effect of Damping,” Proceedings International Symposium on FSI, AE&FIV + N, Dallas, TX, Vol. I, ASME, New York, pp. 29–38.
16.
Seyranian
A. P.
,
1990
, “
Destabilization Paradox in Stability Problems of Nonconservative Systems
,”
Advances in Mechanics (Warszawa)
, Vol.
13
, pp.
89
124
.
17.
Seyranian, A. P., and Pedersen, P., 1995, “On Two Effects in Fluid/Structure Interaction Theory,” Flow-Induced Vibration, Bearman, ed, Balkema, Rotterdam, pp. 565–576.
18.
Thomson, W., and Tait, P. G., 1879, A Treatise on Natural Philosophy, Vol. 1, Part I, New Ed., Cambrige University Press, Cambridge, UK, pp. 387–391.
19.
Triantafyllou
G. S.
,
1992
, “
Physical Condition for Absolute Instability in Inviscid Hydroelastic Coupling
,”
Physics of Fluids A
, Vol.
3
, pp.
544
552
.
This content is only available via PDF.
You do not currently have access to this content.