Page 364 - Fluid-Structure Interactions Slender Structure and Axial Flow (Volume 1)

344 SLENDER STRUCTURES AND AXIAL FLOW

Y

P2 =

Figure 5.27 Codimension-2 bifurcation diagrams for the doubly degenerate system of Figure 5.23:
(a) for cases 1 and 3, defined in (5.125), from Guckenheimer & Holmes (1983); (b) for case 2
(Pa’idoussis & Semler 1993b).
have not been successful. In Figure 5.27 it is seen that most of the limit sets are unstable.
On the other hand, by numerical integration of the equations it is possible to find only
the stable hyperbolic sets.
The heteroclinic orbit on the line 12 = +1(c - l)/b + 1 is of special interest. It is
known that if perturbed, it may give rise to heteroclinic tangles and chaos (Guckenheimer
& Holmes 1983; Moon 1992). This is discussed in more detail in Section 5.8.
fc) 3-0 motions of the doubly degenerate pipe-spring system

Two studies on the three-dimensional motions of the system were conducted by Steindl
& Troger (1988, 1994, 1995), utilizing the equations of motion of Lundgren er al. (1979).