Response statistics of nonlinear systems to parametric filtered white noise

1996 ◽  
pp. 105-129 ◽  
Author(s):  
R Ibrahim ◽  
Y Yoon
Keyword(s):  
Nonlinear Systems ◽  
White Noise

Exact Stationary Response Solution for Second Order Nonlinear Systems Under Parametric and External White Noise Excitations: Part II

1988 ◽  
Vol 55 (3) ◽  
pp. 702-705 ◽  
Author(s):  
Y. K. Lin ◽  
Guoqiang Cai
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Probability Distribution ◽  
White Noise ◽  
Probability Density ◽  
Detailed Balance ◽  
Stationary Probability ◽  
Probability Flow ◽  
Parametric And External Excitations ◽  
White Noises

A systematic procedure is developed to obtain the stationary probability density for the response of a nonlinear system under parametric and external excitations of Gaussian white noises. The procedure is devised by separating the circulatory portion of the probability flow from the noncirculatory flow, thus obtaining two sets of equations that must be satisfied by the probability potential. It is shown that these equations are identical to two of the conditions established previously under the assumption of detailed balance; therefore, one remaining condition for detailed balance is superfluous. Three examples are given for illustration, one of which is capable of exhibiting limit cycle and bifurcation behaviors, while another is selected to show that two different systems under two differents sets of excitations may result in the same probability distribution for their responses.

First-passage problem for nonlinear systems under Lévy white noise through path integral method

2016 ◽  
Vol 85 (3) ◽  
pp. 1445-1456 ◽  
Author(s):  
Christian Bucher ◽  
Alberto Di Matteo ◽  
Mario Di Paola ◽  
Antonina Pirrotta
Keyword(s):  
Nonlinear Systems ◽  
White Noise ◽  
Path Integral ◽  
Integral Method ◽  
First Passage ◽  
Lévy White Noise ◽  
Path Integral Method ◽  
First Passage Problem

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.

scholarly journals Analysis of exceedance probability of displacement response of randomly nonlinear structures

2000 ◽  
Vol 22 (4) ◽  
pp. 212-224 ◽  
Author(s):  
Luu Xuan Hung
Keyword(s):  
Probability Density Function ◽  
Nonlinear Systems ◽  
White Noise ◽  
Probability Density ◽  
Density Function ◽  
Exceedance Probability ◽  
Nonlinear Structures ◽  
Exact Probability ◽  
Displacement Response ◽  
Linearization Techniques

The paper presents the estimation of the exact exceedance probability (EEP) of stationary responses of some white noise-randomly excited nonlinear systems whose exact probability density function can be known. Consequently, the approximate exceedance probabilities (AEPs) are evaluated based on the analysis of equivalent linearized systems using the traditional Caughey method and the extension technique of LOMSEC. Comparisons of the AEPs versus the EEP are demonstrated. The obtained results indicate important characters of the exceedance probability (EP) as well as the influence of nonlinearity over EP. The evaluation of the applied possibility of the proposed linearization techniques for estimating AEPs are made.

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