Stationary response of Duffing-van del Pol oscillator with fractional derivative under wide-band noise excitations

2013 ◽  
Vol 43 (5) ◽  
pp. 670-677
Author(s):  
HaiFeng LI ◽  
LinCong CHEN ◽  
ZhongShen LI ◽  
WeiQiu ZHU
Keyword(s):  
Fractional Derivative ◽  
Wide Band ◽  
Stationary Response ◽  
Band Noise ◽  
Wide Band Noise

Stochastic Averaging of Strongly Nonlinear Oscillators Under Combined Harmonic and Wide-Band Noise Excitations

2008 ◽  
Vol 130 (5) ◽  
Author(s):  
Y. J. Wu ◽  
W. Q. Zhu
Keyword(s):  
Probability Density ◽  
Wide Band ◽  
Nonlinear Oscillators ◽  
Stochastic Averaging ◽  
Random Excitation ◽  
Stationary Response ◽  
Strongly Nonlinear ◽  
Band Noise ◽  
Wide Band Noise ◽  
Strongly Nonlinear Oscillators

Physical and engineering systems are often subjected to combined harmonic and random excitations. The random excitation is often modeled as Gaussian white noise for mathematical tractability. However, in practice, the random excitation is nonwhite. This paper investigates the stationary response probability density of strongly nonlinear oscillators under combined harmonic and wide-band noise excitations. By using generalized harmonic functions, a new stochastic averaging procedure for estimating stationary response probability density of strongly nonlinear oscillators under combined harmonic and wide-band noise excitations is developed. The damping can be linear and (or) nonlinear and the excitations can be external and (or) parametric. After stochastic averaging, the system state is represented by two-dimensional time-homogeneous diffusive Markov processes. The method of reduced Fokker–Planck–Kolmogorov equation is used to investigate the stationary response of the vibration system. A nonlinearly damped Duffing oscillator is taken as an example to show the application and validity of the method. In the case of primary external resonance, based on the stationary joint probability density of amplitude and phase difference, the stochastic jump of the Duffing oscillator and P-bifurcation as the system parameters change are examined for the first time. The agreement between the analytical results and those from Monte Carlo simulation of original system shows that the proposed procedure works quite well.

scholarly journals Optimal Bounded Control for Stationary Response of Strongly Nonlinear Oscillators under Combined Harmonic and Wide-Band Noise Excitations

2011 ◽  
Vol 2011 ◽  
pp. 1-21 ◽  
Author(s):  
Yongjun Wu ◽  
Changshui Feng ◽  
Ronghua Huan
Keyword(s):  
Joint Probability ◽  
Wide Band ◽  
Nonlinear Oscillators ◽  
Stochastic Averaging ◽  
Bounded Control ◽  
Stationary Response ◽  
Strongly Nonlinear ◽  
Band Noise ◽  
Wide Band Noise ◽  
Strongly Nonlinear Oscillators

We study the stochastic optimal bounded control for minimizing the stationary response of strongly nonlinear oscillators under combined harmonic and wide-band noise excitations. The stochastic averaging method and the dynamical programming principle are combined to obtain the fully averaged Itô stochastic differential equations which describe the original controlled strongly nonlinear system approximately. The stationary joint probability density of the amplitude and phase difference of the optimally controlled systems is obtained from solving the corresponding reduced Fokker-Planck-Kolmogorov (FPK) equation. An example is given to illustrate the proposed procedure, and the theoretical results are verified by Monte Carlo simulation.

Discrimination of different temporal envelope structures of diotic and dichotic target signals within diotic wide-band noise

2005 ◽  
pp. 397-403 ◽  
Author(s):  
Steven van de Par ◽  
Armin Kohlrausch ◽  
Jeroen Breebaart ◽  
Martin McKinney
Keyword(s):  
Wide Band ◽  
Temporal Envelope ◽  
Band Noise ◽  
Wide Band Noise

On linear filtering under dependent wide-band noise

Stochastics ◽  
1988 ◽  
Vol 23 (4) ◽  
pp. 413-437 ◽  
Author(s):  
A. E. Bashirov
Keyword(s):  
Wide Band ◽  
Linear Filtering ◽  
Band Noise ◽  
Wide Band Noise

Pitch Shifts of Tones in Wide‐Band Noise 912–913

1966 ◽  
Vol 40 (5) ◽  
pp. 1203-1203
Author(s):  
Sylvia J. Steiner ◽  
Arnold M. Small
Keyword(s):  
Wide Band ◽  
Band Noise ◽  
Wide Band Noise
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