Page 182 - Fluid-Structure Interactions Slender Structure and Axial Flow (Volume 1)

164 SLENDER STRUCTURES AND AXIAL FLOW

load, rather than a pipe conveying fluid. It is seen that (i) for selected combinations of
K and K*, only flutter occurs; (ii) for a given K* # 0, if K is small (K < ~3 in the figure),
the system loses stability by divergence, and again if K is relatively large (K > KZ). The
physical mechanism must be that, for some combinations of (K, K*), the eigenmodal
shapes hinder the development of divergence, while being particularly propitious for
flutter (Section 3.2.2), and so flutter develops rather than divergence.

3.6.3 Pipes with additional point masses

A very interesting study on the effect of lumped masses on the stability of cantilevered
pipes conveying fluid has been made by Hill & Swanson (1970). The system is shown in
Figure 3.67(a), and generally has several point masses at various locations, numbered as
shown. In the equation of motion, equation (3.1), the term rn(a2w/at2) is now replaced by

(3.123)

iZ

m

.. . . . .. ... ..

Figure 3.67 A cantilevered pipe conveying fluid (a) with three point masses added at x,, xz, n3;
(b) with one mass eccentrically located at xj.