HIGHER-ORDER AVERAGING FOR PERIODICALLY FORCED WEAKLY NONLINEAR SYSTEMS

1999 ◽  
Vol 09 (03) ◽  
pp. 519-531 ◽  
Author(s):  
K. YAGASAKI ◽  
T. ICHIKAWA
Keyword(s):  
Nonlinear Systems ◽  
Computer Algebra ◽  
Computer Algebra System ◽  
Higher Order ◽  
Subharmonic Resonance ◽  
Degree Of Freedom ◽  
Weakly Nonlinear ◽  
Lie Transforms ◽  
Two Degree Of Freedom

We consider periodically forced, weakly nonlinear systems and perform higher-order averaging analyses. Especially, we describe an algorithm for computing the higher-order averaging terms by the Lie transforms. The necessary computations can be implemented on a developed package of the computer algebra system, Mathematica. We also give three examples for two Duffing-type oscillators with the primary or ultra-subharmonic resonance and a two-degree-of-freedom system with internal and external resonances, to demonstrate our results.

scholarly journals The influence of nonlinear terms in mechanical systems having two degrees of freedom

2006 ◽  
Vol 28 (3) ◽  
pp. 155-164
Author(s):  
Nguyen Duc Tinh
Keyword(s):  
Nonlinear Systems ◽  
White Noise ◽  
Degrees Of Freedom ◽  
Averaging Method ◽  
Duffing Oscillator ◽  
Stochastic Averaging ◽  
Stochastic Averaging Method ◽  
Higher Order ◽  
White Noise Excitation ◽  
Two Degree Of Freedom

For many years the higher order stochastic averaging method has been widely used for investigating nonlinear systems subject to white and coloured noises to predict approximately the response of the systems. In the paper the method is further developed for two-degree-of-freedom systems subjected to white noise excitation. Application to Duffing oscillator is considered.

Identification of Equivalent Modal Damping and Frequencies in Multi Degree-of-Freedom Nonlinear Systems

2011 ◽  
Author(s):  
D. Dane Quinn ◽  
Richard J. Ott ◽  
Sean Hubbard ◽  
D. Michael McFarland ◽  
Lawrence A. Bergman ◽  
...  
Keyword(s):  
Nonlinear Systems ◽  
Time History ◽  
Degree Of Freedom ◽  
Vibration Absorber ◽  
Primary System ◽  
Vibration Modes ◽  
Structural System ◽  
Modal Damping ◽  
History Of ◽  
Two Degree Of Freedom

We consider the response of a linear structural system when coupled to an attachment containing strong or even essential nonlinearities. For this system, the attachment is designed as a nonlinear vibration absorber, serving to dissipate energy from the structural system. Moreover, the attachment not only leads to a reduction in the total energy of the system, but also couples together the vibration modes of the linear structural system, thereby allowing for energy to also be redistributed among these structural modes of the system. The effect of the nonlinear attachment on the linear primary system can be quantified in terms of equivalent measures for the damping and frequency of each mode, derived through consideration of the energy in each mode. The identification of these equivalent measures is illustrated on a two degree-of-freedom primary system. Moreover, this procedure depends only on the time history of the response and is therefore suited to both simulation and experimental results.

scholarly journals Higher order stochastic averaging method for mechanical systems having two degrees of freedom

2004 ◽  
Vol 26 (2) ◽  
pp. 103-110
Author(s):  
Nguyen Duc Tinh
Keyword(s):  
Degrees Of Freedom ◽  
Averaging Method ◽  
Stochastic Averaging ◽  
Stochastic Averaging Method ◽  
Higher Order ◽  
Degree Of Freedom ◽  
Approximation Solution ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Two Degree Of Freedom

Higher order stochastic averaging method is widely used for investigating single-degree-of-freedom nonlinear systems subjected to white and coloured random noises.In this paper the method is further developed for two-degree-of-freedom systems. An application to a system with cubic damping is considered and the second approximation solution to the Fokker-Planck (FP) equation is obtained.

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