Page 490 - Fluid-Structure Interactions Slender Structure and Axial Flow (Volume 1)

460 SLENDER STRUCTURES AND AXIAL FLOW

I

Figure 6.24 Curved pipes with one end clamped and the other sliding: (a) transverse sliding;
(b)-(d) three variants of axial sliding.

motion are the same as for clamped-clamped pipes; hence, out-of-plane motions will not
be discussed here further.

6.6.1 Transversely sliding downstream end
The dynamics of this system is very similar to that of clamped-clamped pipes, showing:
(a) very slight variation of the eigenfrequencies with flow, and (b) no loss of stability as
-
u is increased. This is surprising at first sight. However, on reflection this is not quite so,
since (i) the steady forces prevent loss of stability by divergence in a similar way as for
clamped-clamped pipes, and (ii) the slope at the sliding end remains zero and hence, by
similarity to straight cantilevered pipes, the system cannot develop flutter.

6.6.2 Axially sliding downstream end

A typical Argand diagram obtained by the modified inextensible theory for in-plane
motions of a quarter-circular pipe conveying fluid and supported as in Figure 6.24(b) is
shown in Figure 6.25. It is seen that the system loses stability by divergence at E$ 2 3.7
and by flutter at ETf 2: 6.0. The dynamics of a semi-circular pipe is qualitatively similar,