The bifurcation diagram
in Figure 12 was realized as follows.
The bifurcation diagrams
and phase portraits of (17) are shown in Figure 3.
Caption: Figure 11: Bifurcation diagram
of system (2) with a = 0.0000001.
When the thickness of the honeycomb core cells changes to 0.0012 m and other parameters are kept the same, the bifurcation diagram
with in-plane force changing has been presented in Figure 7.
Thus, based on the bifurcation diagram
, the waveform, phase portraits, and the power spectrum are utilized to further verify the existence of the chaotic and periodic motion of the blade.
In Figure 3, we firstly fix b = 3 and plot the bifurcation diagram
with respect to a and the related largest Lyapunov exponent.
The Lyapunov exponent spectrum of system in (1) varying with initial condition [l.sub.1] = [w.sub.1o] is shown in Figure 4(a), and the corresponding bifurcation diagram
for y(t) is illustrated as Figure 4(b) with [l.sub.1] [euro] [-5, 5].
Caption: Figure 5: Bifurcation diagram
for illustrating the coexistence of disconnected chaotic attractors with a pair of period-2 limit cycle.
Caption: FIGURE 3: Bifurcation diagram
of Rossler system for [[beta].sub.1] = [[beta].sub.2] = 0.2 using (a) Poincare map and (b) largest Lyapunov exponent.
Caption: Figure 8: Bifurcation diagram
for the system when the amplitude of the road excitation, [??], is 0.05 m: (a) [OMEGA] = 7.96 rad/s to 40 rad/s, (b) [OMEGA] = 7.96 rad/s to 8.25 rad/s.
We see that once [lambda] increases beyond a certain value, the bifurcation diagram
predicts multiple solution.