The First Passage Problem: Duffing Equation

by Aik-Siong Koh, Texas Tech Univ, United States,
Der-Chyan Lin, Texas Tech Univ, United States,

Document Type: Proceeding Paper

Part of: Probabilistic Methods in Civil Engineering


The paper shows some simulation results for the response of the Duffing Equation to stationary Gaussian white noise. Results for the zero-start, double barrier, first passage problem of the equation are also shown. All literature on the stochastic Duffing Equation have used only the positive cubic nonlinearity (hardening stiffness) because the negative cubic nonlinearity (softening and negative stiffness) is intractable analytically. The case of negative stiffness, however, exists in the rocking and toppling of rigid blocks subjected to random forces. Some results are shown for various values of both cases.

Subject Headings: Stiffening | Vibration | Structural analysis | Stochastic processes | Statistics | Stationary processes | Oscillations

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