Page 147 - Fluid-Structure Interactions Slender Structure and Axial Flow (Volume 1)

PIPES CONVEYING FLUID: LINEAR DYNAMICS I 129

- 2AlA3 COS(& - &)I.

Broadly, the centrifugal force imparts energy to the system, while the Coriolis force
(involving B) absorbs energy, the balance between the two, in the absence of dissipation,
giving rise to flutter (Section 3.2.2). However, as discussed in Section 3.5.6, the flutter
mode shape remains broadly similar with varying p, though the mode content is clearly
altered. Hence, as B is increased, the amplitude and phase of the qr components have
to be adjusted to provide a composite shape capable of absorbing energy from the fluid.
For low enough B, 41 and q2 are quite sufficient. However, as B 2 is approached, the
third component, q3, has to come in to achieve the required modal mix; and similarly q4
for Bs~, and q5 for Bs~.
This leaves unanswered the question of why this adjustment in modal content is not
gradual but rather abrupt. The answer is furnished by the phase information, Figure 3.42.

0. I 0.2 0.3 0.4 0.5 0.6

- - (I = 0.01

0.1 0.2 0.3 0.4 0.5 0.6

0. I 0.2 0.3 0.4 0.5 0.6
B

Figure 3.42 The evolution of phase differences between the generalized coordinates qr associated
with the Galerkin discretization of the horizontal cantilevered pipe system, as a function of B.