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 [27], 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.
