Subharmonic vibrations of order 1/2, and almost periodic oscillations of a nonlinear vibrating system with a restoring characteristic of the Duffing type and a retardation

1989 ◽  
Vol 4 (6) ◽  
pp. 453-463
Author(s):  
Y. Tsuda ◽  
A. Sueoka ◽  
H. Tamura ◽  
Y. Yoshitake
Keyword(s):  
Almost Periodic ◽  
Periodic Oscillations ◽  
Vibrating System

Asymptotically Stable Almost-Periodic Oscillations in Systems with Hysteresis Nonlinearities

2000 ◽  
Vol 19 (2) ◽  
pp. 469-487 ◽  
Author(s):  
M. Brokate ◽  
I. Collings ◽  
A.V. Pokrovskii ◽  
F. Stagnitti
Keyword(s):  
Asymptotically Stable ◽  
Almost Periodic ◽  
Periodic Oscillations

Almost-periodic oscillations in double-tuned damped system

1980 ◽  
Vol 32 (2) ◽  
pp. 155-158
Author(s):  
A. S. Ponomarev
Keyword(s):  
Almost Periodic ◽  
Periodic Oscillations ◽  
Damped System

scholarly journals Generalizing the Multimodal Method for the Levitating Drop Dynamics

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
M. O. Chernova ◽  
I. A. Lukovsky ◽  
A. N. Timokha
Keyword(s):  
Free Surface ◽  
Almost Periodic ◽  
Modal System ◽  
Periodic Oscillations ◽  
Weakly Nonlinear ◽  
Modal Theory ◽  
Drop Dynamics ◽  
Finite Dimensional ◽  
Multimodal Method ◽  
Good Agreement

The present paper extends the multimodal method, which is well known for liquid sloshing problems, to the free-surface problem modeling the levitating drop dynamics. The generalized Lukovsky-Miles modal equations are derived. Based on these equations an approximate modal theory is constructed to describe weakly-nonlinear axisymmetric drop motions. Whereas the drop performs almost-periodic oscillations with the frequency close to the lowest natural frequency, the theory takes a finite-dimensional form. Periodic solutions of the corresponding finite-dimensional modal system are compared with experimental and numerical results obtained by other authors. A good agreement is shown.

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