Through three sets of bifurcation diagrams, we find that breathing crack plate has complex nonlinear phenomena such as quasi-periodic motion
, bifurcation motion, and chaotic motion, and the nonlinear dynamic behaviors of open-crack model are similar to intact plate model, which merely presents the single-cycle motion and the double periodic motion
1], that means that the dynamic state is under periodic motion
, then judging the periodicity by comparing with [[epsilon].
Fluctuations close to periodic motion
of self-oscillating systems.
Combining s-v phase diagram and Poincare section, it can be got that the response is the periodic motion
at [omega] = 775 Hz.
b) Melnikov method is used in case of periodic motions
and is analysing the conditions necessary in order for the stable and non-stable varieties of the same hyperbolic point to transversally intersect each odder.
The periodic motion
of the sphere behind the advancing free surface is obvious from this plot.
Heller, now at Harvard University, argued on theoretical grounds that quantum particles in such a geometry would have eigenfunctions that retain some of the wave patterns associated with regular, periodic motion
rotor) performs a periodic motion
, which is defined by the following law :
Taking advantage of a chaotic system's extreme sensitivity to initial conditions, they use a series of tiny, judiciously chosen and carefully applied perturbations to maneuver its behavior into the type of periodic motion
It is well known that the periodic motion
of the Earth's spin axis in terrestrial frame (polar motion) is dominantly dictated by geophysical excitations (mainly caused by the motions of the atmosphere and oceans).
It clearly exhibits the hallmark of a chaotic system -- that is, getting continuously thrown from one periodic motion
to another," Rauseo says.
According to their simple model, gusts of wind initially act as a random buffeting force on a suspension bridge, causing the towers and main cable to go into a high-frequency periodic motion
like that of a randomly struck guitar string.
At other times, I can get it doing simple periodic motion
[like a pendulum] or more complicated periodic motions
After a literature survey of analytical methods in nonlinear dynamical systems, he covers the analytical bifurcation trees of period-m motion to chaos for Duffing oscillator, the period-m motion in the periodically forced van del Pol oscillator, the analytical bifurcation trees of period motions to chaos in the van del Pol-Duffing oscillator, the analytical solutions of period-m motions in parametric nonlinear oscillators, and the bifurcation tree of periodic motions
to chaos in a nonlinear Jeffcott rotor dynamic system.
In the second concept, crosswind AWE systems, high-speed periodic motions
of a kite-like tethered wing are used and the generator is ground-based.