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PIPES CONVEYING FLUID: NONLINEAR AND CHAOTIC DYNAMICS 393
2.5
4
14 -1.8 -1.6 -1.4 -1.2 -1.0
1.5 - 13
0.4
0.2
81 0.5 -
0.0 8,
-0.2
4.4
-0.6
4.5 5.0 5.5 6.0
(a) U (b)
*
I‘ I I I I I I I I I
3.4 3.8 4.2 4.6 5.0
(C) U
Figure 557 (a) A bifurcation diagram for the first-segment angle 81 versus u for an initially
‘deformed’ articulated cantilever with $ = 0.6 (defined in Section 5.8.5): -, stable orbits; ---,
unstable orbits. (b) Portion of a period-(1, 5) orbit at u = 5.15; for the large orbit, 81, $1 lie within
(-3,2). (c) Map showing the areas of dynamical behaviour defined in Table 5.8; homl stands for
the principal E-homoclinic orbits (Champneys 1991, 1993).