Control of Limit Cycle Oscillation Amplitudes in Nonlinear Aerelastic Systems using Nonlinear Normal Modes

2016 ◽  
Author(s):  
Himanshu Shukla ◽  
Mayuresh Patil
Keyword(s):  
Limit Cycle ◽  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Limit Cycle Oscillation ◽  
Cycle Oscillation ◽  
Nonlinear Normal

An Application of the Poincare´ Map to the Stability of Nonlinear Normal Modes

1980 ◽  
Vol 47 (3) ◽  
pp. 645-651 ◽  
Author(s):  
L. A. Month ◽  
R. H. Rand
Keyword(s):  
Floquet Theory ◽  
Poincaré Map ◽  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Theory Approach ◽  
Poincare Map ◽  
Linearized Stability ◽  
Nonlinear Normal ◽  
The Stability ◽  
Two Degree Of Freedom

The stability of periodic motions (nonlinear normal modes) in a nonlinear two-degree-of-freedom Hamiltonian system is studied by deriving an approximation for the Poincare´ map via the Birkhoff-Gustavson canonical transofrmation. This method is presented as an alternative to the usual linearized stability analysis based on Floquet theory. An example is given for which the Floquet theory approach fails to predict stability but for which the Poincare´ map approach succeeds.

Localized and Non-Localized Normal Modes in a Strongly Nonlinear Discrete System

1991 ◽  
Author(s):  
Alexander F. Vakakis
Keyword(s):  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Linear Vibration ◽  
Mode Localization ◽  
Linear Mode ◽  
Strongly Nonlinear ◽  
System A ◽  
Coupling Stiffness ◽  
Nonlinear Normal ◽  
Nonlinear Discrete System

Abstract The free oscillations of a strongly nonlinear, discrete oscillator are examined by computing its “nonsimilar nonlinear normal modes.” These are motions represented by curves in the configuration space of the system, and they are not encountered in classical, linear vibration theory or in existing nonlinear perturbation techniques. For an oscillator with weak coupling stiffness and “mistiming,” both localized and nonlocalized modes are detected, occurring in small neighborhoods of “degenerate” and “global” similar modes of the “tuned” system. When strong coupling is considered, only nonlocalized modes are found to exist. An interesting result of this work is the detection of mode localization in the “tuned” periodic system, a result with no counterpart in existing theories on linear mode localization.

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