Abstract
A new approach for efficient numerical implementation of the path integral (PI) method based on non-Gaussian transition probability density function (PDF) and the Gauss-Legendre integration scheme is developed. The PI method is used to solve the Fokker-Planck (FP) equation and to study the nature of the stochastic and chaotic response of the nonlinear systems. The steady state PDF, jump phenomenon, noise induced state changes of PDF are studied by the method. A computationally efficient higher order, finite difference (FD) technique is derived for the solution of higher dimensional FP equation. A two degree of freedom (DOF) nonlinear system having Coulomb damping with variable friction coefficient is considered representative of bladed disk assembly of turbo-machinery blades. Effects of normal force and viscous damping on the mean square response of a blade are investigated.
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Narayanan, S., Kumar, P. (2011). Numerical Solution of Fokker-Planck Equation for Nonlinear Stochastic Dynamical Systems. In: Zhu, W.Q., Lin, Y.K., Cai, G.Q. (eds) IUTAM Symposium on Nonlinear Stochastic Dynamics and Control. IUTAM Bookseries, vol 29. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0732-0_8
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DOI: https://doi.org/10.1007/978-94-007-0732-0_8
Publisher Name: Springer, Dordrecht
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