Figure 5 shows periodic motions
when the in-plane load [P.sub.1] = -260 Pa.
Since we can control the responses of the system from the chaotic motions to the periodic motions
by changing the perturbation rotating speed, we can control the large amplitude nonlinear vibrations of the blade.
The fact that the Lyapunov dimension is an integer means that the system has periodic motion
. When parameter [OMEGA] increases beyond the bifurcation point (such as when [OMEGA] = 7.964 rad/s), the Lyapunov exponents are [[lambda].sub.1] = 0.0054396 and [[Lambda].sub.2] = -0.092153, and the Lyapunov dimension is [d.sub.L] = 1.059.
The Second Case Periodic Motion
. For the gear transmission system, the second case periodic motion
that corresponds to the collision state of the gear can be divided into two cases: single-sided impact periodic motions
and double-sided impact periodic motions
Gegg, "On the mechanism of stick and non-stick periodic motion
in a periodically forced, linear oscillator with dry friction," ASME Journal of Vibration and Acoustics, vol.
The Lorenz-Stenflo system has many dynamical behaviors that are one chaotic motion and six different periodic motions
as shown in Figure 1.
At the same time, theory fixed point of the n - 1 periodic motion
is given by
Fluctuations close to periodic motion
of self-oscillating systems.
It is also found that the system enters into periodic motion
from chaotic motion when the piezoelectric parameter [[alpha].sub.25] increases from 1.0 to 2.0.
As can be seen from Figure 4(a), the top Lyapunov exponent turns out to be [[lambda].sub.1] = -0.052549, which is negative, and the periodic motion
of the system can be detected as presented in Figure 4(d).
In , Hartog initially made an investigation on the periodic motion
of the forced linear oscillator with Coulomb and viscous damping.
The bifurcation results show that the system behaves as 1T-periodic motion at low mesh frequency and the periodic motion
persists until [[omega].sub.h] > 0.425.