A consistent closure method for non-linear random vibration

Mircea Dan Grigoriu

11 citations0/0 files storedInternational Journal of Non-Linear Mechanics

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Probabilistic and Robust Engineering Design Control Systems and Identification stochastic dynamics and bifurcation

Abstract

—A closure method is proposed for calculating moments of the state vector of a non-linear system satisfying an Itô stochastic differential equation. It is based on a finite set of moment equations and a sequence of probabilities converging to the exact distribution of the state vector that is obtained by the minimization of an objective function. Numerical results for one-dimensional diffusion processes show that the proposed closure technique is robust in the sense that resultant moments are satisfactory even when crude approximations are used for the probability of the state vector.

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1987Probability Densities of the Response of Non-Linear Structures under Stochastic Dynamic Excitation 1989Probability densities of the response of nonlinear structures under stochastic dynamic excitation

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