When parameter [OMEGA] exists in region B, quasiperiodic motion
occurs in this region.
That is, the DE experiences a dynamic stability evolution from an aperiodic motion to the quasiperiodic motion for a relative high frequency.
The system of the viscoelastic DE also presents stability transition from an aperiodic motion to the quasiperiodic motion for a relative high frequency and experiences a stability evolution from single cycle motion to multicycle motion with the increasing relaxation times for a fixed frequency.
When [k.sub.s-av] <1 x [10.sup.7] N/m, the response amplitude is at stable state and the system tends to do quasiperiodic motion
The s-v phase diagram is made up by many closed curves combining with Poincaree section, and it can be indicated that the response of pipe wall is the quasiperiodic motion.
These all showed that the response of pipe wall is the quasiperiodic motion.
And from the bifurcation diagram, it can be speculated that the response of pipe wall would be alternately in quasiperiodic motion, multiperiod motion, and even chaos motion.
As we all know, the power spectrum of periodic motion gives peaks at a primary frequency and its harmonics, and the power spectrum of quasiperiodic motion
gives peaks at linear combinations of two or more irrationally related frequencies, and the power spectrum of chaotic motion gives continuous broadband components to the spectrum.
To conclude, the rotors execute four-period quasiperiodic motion
around critical speeds, Figures 10,11,16, and 17.
For the cutting process, the periodic motion is named stability state, and other motions are named instability states including quasiperiodic motion and chaotic motion.
The movement state of tool point is chaos in the beginning when the speed is round 1000 r/min, then becomes quasiperiodic motion gradually as the speed increases to 7000 r/min, and finally tends to be stable periodic motion similarly with the speed continuing to rise up.
The system is a quasiperiodic motion by lots of combination frequencies of inherence frequency and rotating frequency in the amplitude spectrum and a closed pattern in Poincare: mapping.