Page 76 - Fluid-Structure Interactions Slender Structure and Axial Flow (Volume 1)

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Pipes Conveying Fluid:

Linear Dynamics I

3.1 INTRODUCTION
The study of dynamics of pipes conveying fluid has a fine pedigree. A series of exper-
iments by Aitken (1 878) on travelling chains and elastic cords, illustrating the balance
between motion-induced tensile and centrifugal forces in this momentum transport system,
is perhaps among the earliest work pertinent to the topic at hand. Self-excited oscillations
of a cantilevered pipe conveying fluid had been observed by Brillouin as far back as 1885
(Bourri2res 1939), but remained unpublished “duns me Note de luborutoire ”.
The first serious study of the dynamics of pipes conveying fluid is due to Bourrikres
(1939), who derived the correct equations of motion and carried its analysis remarkably
far, reaching admirably accurate conclusions regarding stability, in particular concerning
the cantilevered system. This study, published in the year of the outbreak of the Second
World War, was effectively ‘lost’, and researchers rederived everything in ignorance of
its existence in the 1950s and 1960s. Bourrikres’ work was rediscovered by the author in
1973 in the course of delivering a seminar in France, thanks to a comment by Professor
A. Fortier of the University of Paris who was in attendance (PaYdoussis & Issid 1974).
Certainly, some aspects of the problem have been known for a long time and are in
almost everyone’s common experience. Thus, the buckling (divergence) of a pipe with
both ends supported, manifested by the large restraining force that must be exerted by those
holding a fire-hose at high discharge rates, is also experienced, albeit highly diminished,
by one watering the lawn. Thejutter of a cantilevered pipe, manifested by the thrashing,
snaking motions of a fire-hose accidentally released or by a garden-hose when dropped
on the wet grass, is well known to firemen and amateur gardeners alike. In fact, these
two phenomena are often, irreverently but graphically, referred to as the $re-hose and
garden-hose instability, respectively.
Nevertheless, the subject is far from being of the ‘garden variety’ sort. Indeed this has
become a new model problem in the study of dynamics and stability of structures, on a
par with the classical problems of a column subjected to compressive loading and the
rotating shaft (Paidoussis & Li 1993). Some reasons why this is so are the following:
(i) it is a physically simple system, easily modelled by simple equations, yet capable of
displaying a kaleidoscope of interesting dynamical behaviour, both linear and nonlinear;
(ii) it is a fairly easily realizable system, thus affording the possibility of theoretical
and experimental investigation in concert; (iii) in its many variants, it is a more general
problem, with richer dynamical behaviour, than that of the column and in some ways

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