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190 SLENDER STRUCTURES AND AXIAL FLOW

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Figure 3.79 (continued).

Further theoretical and experimental results may be found in Paldoussis & Deksnis
(1969, 1970). The final conclusions are the following. First, there is, after all, a smooth
transition between the discrete system, as N is increased, and the continuously flexible
one. Second, the low-N discrete system dynamics can be quite different from those of
the continuous system [Figure 3.79(b)], and hence the popular two-degree-of-freedom
articulated ‘models’, which work so well for Coriolis-free follower-force nonconservative
systems, should be used with caution in the case of pipes conveying fluid if the results
are meant to be extrapolated to those of the continuous system.

3.8.3 Modified systems
A very extensive and systematic study of various modified two-degree-of-freedom articu-
lated cantilevered systems has been undertaken by Sugiyama and co-workers - ‘modified’
in a similar way as the continuous systems discussed in Section 3.6, by the addition of
springs, masses, and so on.