Page 421 - Fluid-Structure Interactions Slender Structure and Axial Flow (Volume 1)
P. 421

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).
   416   417   418   419   420   421   422   423   424   425   426