Page 429 - Fluid-Structure Interactions Slender Structure and Axial Flow (Volume 1)

PIPES CONVEYING FLUID: NONLINEAR AND CHAOTIC DYNAMICS 401

0.012

0.000
0.2 0.3 0.4
P

0.0 I4

0.002 1 I I I 1 I I
0.55 0.60 0.65 0.70 0.75
/*

-0.015 0.01 8
(C) 91
Figure 5.61 One-degree-of-freedom approximation of the dynamics of a pinned-pinned pipe
(/3 = 0.78, y = 15.48, a = 0, o = 0.883, SA = 1.81 x IO4, Ug = 3.1385) subjected to pulsating
flow: (a) the amplitude versus p diagram for wg = 8.8 via the multiple scales method; (b,c) numer-
ical results for wo = 8.875 showing the bifurcation diagram and period-8 motion in the phase plane
for ,u = 0.7123 (Jayaraman & Narayanan 1996).