Stabilization via parametric excitation of multi-dof statically unstable systems

2014 ◽  
Vol 19 (10) ◽  
pp. 3913-3926 ◽  
Author(s):  
Inga M. Arkhipova ◽  
Angelo Luongo
Keyword(s):  
Parametric Excitation ◽  
Unstable Systems

Stabilization of statically unstable systems by parametric excitation

2009 ◽  
Vol 323 (3-5) ◽  
pp. 1016-1031 ◽  
Author(s):  
Alexei A. Mailybaev ◽  
Alexander P. Seyranian
Keyword(s):  
Parametric Excitation ◽  
Unstable Systems

Generalized renormalization group treatment of the growth kinetics of unstable systems

1985 ◽  
Vol 41 (1-2) ◽  
pp. 17-36 ◽  
Author(s):  
Scott R. Anderson ◽  
Gene F. Mazenko ◽  
Oriol T. Valls
Keyword(s):  
Renormalization Group ◽  
Growth Kinetics ◽  
Group Treatment ◽  
Unstable Systems ◽  
Kinetics Of

On the Parametric Excitation of Pendulum-Type Vibration Absorber

1961 ◽  
Vol 28 (3) ◽  
pp. 330-334 ◽  
Author(s):  
Eugene Sevin
Keyword(s):  
Energy Transfer ◽  
Numerical Solution ◽  
Parametric Excitation ◽  
Equations Of Motion ◽  
Vibration Absorber ◽  
Single Cycle ◽  
Linearized System ◽  
Nonlinear Equations Of Motion ◽  
Beam Oscillation ◽  
Energy Interchange

The free motion of an undamped pendulum-type vibration absorber is studied on the basis of approximate nonlinear equations of motion. It is shown that this type of mechanical system exhibits the phenomenon of auto parametric excitation; a type of “instability” which cannot be accounted for on the basis of the linearized system. Complete energy transfer between modes is shown to occur when the beam frequency is twice the simple pendulum frequency. On the basis of a numerical solution, approximately 150 cycles of the beam oscillation take place during a single cycle of energy interchange.

Parametric excitation of magnetoacoustic waves by a pump magnetic field in a high-β plasma

1977 ◽  
Vol 17 (1) ◽  
pp. 93-103 ◽  
Author(s):  
N. F. Cramer
Keyword(s):  
Magnetic Field ◽  
Parametric Excitation ◽  
Acoustic Waves ◽  
Magnetic Pressure ◽  
Gas Pressure ◽  
Alfven Wave ◽  
Fast Wave ◽  
Magnetoacoustic Waves ◽  
Background Magnetic Field ◽  
The Waves

The parametric excitation of slow, intermediate (Alfvén) and fast magneto-acoustic waves by a modulated spatially non-uniform magnetic field in a plasma with a finite ratio of gas pressure to magnetic pressure is considered. The waves are excited in pairs, either pairs of the same mode, or a pair of different modes. The growth rates of the instabilities are calculated and compared with the known result for the Alfvén wave in a zero gas pressure plasma. The only waves that are found not to be excited are the slow plus fast wave pair, and the intermediate plus slow or fast wave pair (unless the waves have a component of propagation direction perpendicular to both the background magnetic field and the direction of non-uniformity of the field).

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