Page 439 - Fluid-Structure Interactions Slender Structure and Axial Flow (Volume 1)

PIPES CONVEYING FLUID: NONLINEAR AND CHAOTIC DYNAMICS 41 1

0.15 0.20 0.25 0.30 0.35 0.40

10 20 30 40
(b) Forcing frequency, w
Figure 5.68 (a) Linear stability boundaries for a cantilevered system with uo = 7.68, B = 0.307,
y = 16.1 and CY = 3.65 x (b) Amplitude versus w diagram for p = 0.37: -, primary reso-
nances (w/% 2 2 and $) associated with the second mode; . . ., secondary fundamental resonance
for the second mode (Semler & Paidoussis 1996).
0.41 . I , I , . , , , , , ,

" "-I
=-

IO 15 20 2s 30 35 40
Forcing frequency, w

Figure 5.69 Bifurcation diagram for the principal and fundamental resonances for the system of
Figure 5.66 but with uo = 6.5, obtained with the FDM (Semler & Pdidoussis 1996).