Stochastic Jump and Bifurcation of a Duffing Oscillator Under Narrow-Band Excitation

1993 ◽  
Vol 165 (2) ◽  
pp. 285-304 ◽  
Author(s):  
W.Q. Zhu ◽  
M.Q. Lu ◽  
Q.T. Wu
Keyword(s):  
Narrow Band ◽  
Duffing Oscillator ◽  
Stochastic Jump ◽  
Stochastic Jump And Bifurcation

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.

scholarly journals On double-peak probability density functions of a Duffing oscillator under narrow-band random excitations

2005 ◽  
Vol 54 (6) ◽  
pp. 2557
Author(s):  
Rong Hai-Wu ◽  
Wang Xiang-Dong ◽  
Xu Wei ◽  
Meng Guang ◽  
Fang Tong
Keyword(s):  
Probability Density ◽  
Narrow Band ◽  
Duffing Oscillator ◽  
Probability Density Functions ◽  
Density Functions ◽  
Double Peak

scholarly journals The influence of second order narrow-band colored noises on non-linear random vibrations

1999 ◽  
Vol 21 (2) ◽  
pp. 65-74
Author(s):  
Nguyen Dong Anh ◽  
Nguyen Duc Tinh
Keyword(s):  
Colored Noise ◽  
Averaging Method ◽  
Narrow Band ◽  
Duffing Oscillator ◽  
Stochastic Averaging ◽  
Random Processes ◽  
Stochastic Averaging Method ◽  
Second Order ◽  
External Excitation ◽  
First Order

Since the effect of some nonlinear terms is lost during the first order averaging procedure, the higher order stochastic averaging method is developed to predict approximately the response of linear and lightly nonlinear systems subject to weakly external excitation of second order colored noise random processes. Application to Duffing oscillator is considered.

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