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276 SLENDER STRUCTURES AND AXIAL FLOW

(c) Travelling bands and MAGLEV systems

The close similarity in the dynamics of travelling bands (band-saws, chains, magnetic tape,
deploying antennas in space, etc.) have already been remarked upon on several occasions
in this book; see, e.g. Mote (1968, 1972), Tabarrok et al. (1974), Wickert & Mote (1990).
This is a case where cross-fertilization of ideas and swapping of techniques has been and is
constantly taking place; a good example is given in Section 5.5.1. Another, among many
areas benefitting from such cross-fertilization is magnetic levitation (MAGLEV) vehicle-
guideway systems (Cai et al. 1992, 1996), where divergence and flutter instabilities can
arise (Cai & Chen 1995).
(d) Severed pipes and pipe-whip

In many cases, a pipe may be acceptably ‘stable’ when connected the way it is meant
to be, at both ends. If one end is accidentally disconnected or severed, however, which
may sometimes mean the loss of tension which rendered it stable, the cantilevered pipe
or pipe-string may well be unstable by flutter. Examples of such occurrences relate to
fire-hoses and to life-lines used in space and underwater.
In the same family of accidents is the rupture in a pipe conveying high-pressure
fluid, which causes the fluid to ‘blow down’ through the unevenly ruptured pipe into
the surrounding fluid medium. As a result, the pipe may ‘whip about’, causing damage to
surrounding structures. It is required practice for designers of power plants ‘to postulate
pipe ruptures and then perform analysis to determine what restraints or armor is required
to prevent secondary failures’ (Blevins 1990). A sample calculation of the motion of a
pipe after rupture may be found in Blevins (1990, Chapter 10).

(e) Sprinkler system
A garden-variety type of application is the author’s invention of a novel sprinkler for
a McGill Open House circa 1976. It consists of an elastomer up-standing cantilevered
pipe, mounted on a simple base and connected to the water mains. At the free end, a
coarsely perforated stopper may be used. The hose performs a circular motion and waters
a circular patch of lawn. Although it is not more effective than any other sprinkler, it is
more aesthetically attractive than many, something like kinetic art!

4.8 CONCLUDING REMARKS
Even in an extensive treatment of the subject of the dynamics of straight pipes conveying
fluid such as is given here in Chapters 3, 4 and 5, it is impossible to cite all the work,
let alone discuss it. Hence, a great deal has been left out. Among that is the burgeoning
effort on control of cantilevered pipes in flutter.
Control of the linear system has been studied by Takahashi et al. (1990), Kangaspu-
oskari et al. (1993), Cui et al. (1994, 1995), Tani & Sudani (1995), Lin & Chu (1996),
Tsai & Lin (1997), Doki et al. (1998) and of the nonlinear chaotic system by Yau et al.
(1993, utilizing a wide variety of control schemes. Some of the work, e.g. Tani & Sudani’s
(1995) and by Doki et al. (1998), is supported by experiments.
Some new work has began appearing also on shape optimization to maximize the
critical flow velocity for flutter (Tanaka er al. 1993).