Equivalent linearization of MDOF systems under external Poisson white noise excitation

2002 ◽  
Vol 17 (4) ◽  
pp. 393-399 ◽  
Author(s):  
Carsten Proppe
Keyword(s):  
White Noise ◽  
Equivalent Linearization ◽  
Poisson White Noise ◽  
White Noise Excitation ◽  
Mdof Systems

scholarly journals Dynamics of a Nonlinear Business Cycle Model Under Poisson White Noise Excitation

2015 ◽  
Vol 3 (2) ◽  
pp. 176-183 ◽  
Author(s):  
Jiaorui Li ◽  
Shuang Li
Keyword(s):  
Business Cycle ◽  
White Noise ◽  
Economic System ◽  
Probability Density ◽  
Stationary Probability ◽  
Cycle Model ◽  
Poisson White Noise ◽  
Stationary Probability Density ◽  
White Noise Excitation ◽  
Business Cycle Model

AbstractSeveral observations in real economic systems have shown the evidence of non-Gaussianity behavior, and one of mathematical models to describe these behaviors is Poisson noise. In this paper, stationary probability density of a nonlinear business cycle model under Poisson white noise excitation has been studied analytically. By using the stochastic averaged method, the approximate stationary probability density of the averaged generalized FPK equations are obtained analytically. The results show that the economic system occurs jump and bifurcation when there is a Poisson impulse existing in the periodic economic system. Furthermore, the numerical solutions are presented to show the effectiveness of the obtained analytical solutions.

scholarly journals Stochastic Responses of Lightly Nonlinear Vibroimpact System with Inelastic Impact Subjected to External Poisson White Noise Excitation

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Guidong Yang ◽  
Wei Xu ◽  
Dongmei Huang ◽  
Mengli Hao
Keyword(s):  
White Noise ◽  
Coordinate Transformation ◽  
Perturbation Technique ◽  
Inverse Transformation ◽  
Poisson White Noise ◽  
Dirac Delta ◽  
White Noise Excitation ◽  
Inelastic Impact ◽  
Fpk Equation ◽  
Vibroimpact System

A procedure for analyzing stationary responses of lightly nonlinear vibroimpact system with inelastic impact subjected to external Poisson white noise excitation is proposed. First, the original vibroimpact system is transformed to a new system without velocity jump in terms of the Zhuravlev nonsmooth coordinate transformation and the Dirac delta function. Second, the averaged generalized Fokker-Planck-Kolmogorov (FPK) equation for transformed system under parametric excitation of Poisson white noise is derived by stochastic averaging method. Third, the averaged generalized FPK equation is solved by using the perturbation technique and inverse transformation of the Zhuravlev nonsmooth coordinate transformation to obtain the approximately stationary solutions for response probability density functions of original vibroimpact system. Last, analytical and numerical results for two typical lightly nonlinear vibroimpact systems are presented to assess the effectiveness of the proposed method. It is found that they are in good agreement and the proposed method is quite effective.

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