scholarly journals Some Statistics of Stochastic Jump Phenomena of a Duffing Oscillator to Narrow Band Random Excitation(Mechanical Systems)

2009 ◽  
Vol 75 (754) ◽  
pp. 1560-1567 ◽  
Author(s):  
Shinji TAMURA ◽  
Yasuhiro SUZUKI ◽  
Koji KIMURA
Keyword(s):  
Narrow Band ◽  
Duffing Oscillator ◽  
Mechanical Systems ◽  
Random Excitation ◽  
Stochastic Jump ◽  
Jump Phenomena

Nonlinear Dynamics of a Parametrically Excited Laminated Beam: Narrow-Band Random Excitation

2010 ◽  
Vol 43 ◽  
pp. 257-261
Author(s):  
Xiang Jun Lan ◽  
Zhi Hua Feng ◽  
Xiao Dong Zhu ◽  
Hong Lin
Keyword(s):  
Nonlinear Dynamics ◽  
Finite Difference Method ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Narrow Band ◽  
Joint Probability ◽  
Random Excitation ◽  
Laminated Beam ◽  
Stochastic Jump ◽  
Stochastic Jump And Bifurcation

The first mode parametric resonance of a laminated beam subject to narrow-band random excitation is taken into consideration. The method of multiple scales is used and the stochastic jump and bifurcation have been investigated aiming at the stationary joint probability of the response of the system by using finite difference method. Results show that stochastic jump occurs mainly in the region of triple valued solution. The higher is the frequency, the more probable is the jump from the stationary nontrivial branch to the trivial one, whereas the most probable motion gradually approaches the trivial one when the band width becomes higher.

Primary Resonance of a Duffing Oscillator With Two Distinct Time Delays in State Feedback Under Narrow-Band Random Excitation

2007 ◽  
Author(s):  
Yanfei Jin ◽  
Haiyan Hu
Keyword(s):  
Time Delays ◽  
State Feedback ◽  
Multiple Scales ◽  
Narrow Band ◽  
Damping Ratio ◽  
Duffing Oscillator ◽  
Primary Resonance ◽  
Random Excitation ◽  
Equivalent Damping ◽  
The Difference

The primary resonance of a Duffing oscillator with two distinct time delays in state feedback under narrow-band random excitation is investigated in detail by using the method of multiple scales. First, the equations of modulation of response amplitude and phase are determined. Then, the expressions of the first-order and the second-order steady-state moments and their stable regions are obtained by introducing the equivalent detuning frequency and the equivalent damping ratio. For the case of two distinct time delays, the appropriate choices of the combinations of the feedback gains and the difference between two time delays are discussed from the viewpoint of vibration control. Finally, the theoretical analyses are well verified through numerical simulations.

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