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Large Monte Carlo Simulation of Duffing Equation

by A. -S. Koh, Texas Tech Univ, United States,
D. -C. Lin, Texas Tech Univ, United States,



Document Type: Proceeding Paper

Part of: Structural Safety and Reliability

Abstract:

This effort aims to obtain some accurate statistics of the Duffing Equation subjected to white noise through Monte Carlo simulation. The results obtained can be used to check the accuracy of known or new approximate answers and to help provide insights into the true behavior of the system. Ensemble size of 200,000 records are used to ensure small variances in the statistics collected. The coefficient of cubic nonlinearity is varied, and both positive and negative values of the nonlinear coefficient are used in the investigation. Statistics collected are the time histories of the second and fourth moments of displacement, and the first passage probability densities and survival probabilities for the double barrier type.

Subject Headings: Statistics | Monte Carlo method | Probability | Dynamic structural analysis | Noise pollution | Displacement (mechanics) | Vibration

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