The stochastic analysis of the response of frictionally damped Duffing oscillator subjected to Poisson white noise (PWN) and its stochastic bifurcation analysis are considered. The behaviour of the stochastic attractors is examined through the stationary solution of the corresponding generalized Fokker-Planck-Kolmogorov (FPK) or Kolmogorov-Feller (KF) equation. A finite element (FE) scheme has been used for the solution of the FPK equation, using C1 continuity shape functions. Parametric studies are carried out to gain insights into the effects of the Coulomb friction, and arrival rates of the underlying Poisson process of PWN. The results of FE solution are shown to be in good agreement with the results of Monte Carlo simulation (MCS). © 2016 The Authors.

Sayan Gupta

Department of Applied Mechanics

Bifurcation (mathematics)

finite element method

FOKKER PLANCK EQUATION

Friction

Intelligent systems

Monte Carlo methods

Oscillators (mechanical)

Poisson equation

Stochastic systems

tribology

Coulomb frictions

DUFFING OSCILLATOR

FOKKER-PLANCK-KOLMOGOROV

Friction damper

Poisson Noise

STATIONARY SOLUTIONS

Stochastic analysis

STOCHASTIC BIFURCATION

White noise

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IIT Madras

Procedia Engineering

Nonlinear oscillators subjected to colored Gaussian/non-Gaussian excitations are modelled through a set of three coupled first-order stochastic differential equations by representing the excitation as a first-order filtered white noise. A 3-D finite element (FE) formulation is developed to solve the corresponding 3-D Fokker Planck (FP) equations. The joint probability density functions of the state variables, obtained as a solution of the FP equation, are typically non-Gaussian and are used for computing the crossing statistics of the response - an essential metric for time variant reliability analysis. The method is illustrated through a noisy Lorenz attractor and a Duffing oscillator subjected to additive colored noise. The increase in state-space dimension when the Duffing oscillator is additionally excited with a parametric Gaussian noise is effectively handled by using stochastic averaging to reduce the state-space dimension. Investigations are carried out to examine the accuracy of the FE method vis-a-vis Monte Carlo simulations. The proposed method is observed to be computationally significantly cheaper for these three problems. © 2014 Elsevier Ltd. All rights reserved.

Probabilistic Engineering Mechanics

Finite element solution of Fokker-Planck equation of nonlinear oscillators subjected to colored non-Gaussian noise

Journal of Sound and Vibration

Probabilistic solution of nonlinear oscillators excited by combined Gaussian and Poisson white noises

Path integral solution for non-linear system enforced by Poisson White Noise

International Journal of Non-Linear Mechanics

Erratum to “Monte Carlo simulation in the stochastic analysis of non-linear systems under external stationary Poisson white noise input” [Int. J. Non-Linear Mech. 38 (2003) 1269–1283]

Efficient path integration methods for nonlinear dynamic systems

Stochastic Bifurcation Analysis of a Duffing Oscillator with Coulomb Friction Excited by Poisson White Noise

Journal	Data powered by TypesetProcedia Engineering
Publisher	Data powered by TypesetElsevier Ltd
ISSN	18777058
Open Access	Yes