Response and First-Passage Statistics of Nonlinear Oscillators via a Numerical Path Integral Approach
Publication: Journal of Engineering Mechanics
Volume 139, Issue 9
Abstract
A numerical path integral solution approach is developed for determining the response and first-passage probability density functions (PDFs) of nonlinear oscillators subject to evolutionary broad-band stochastic excitations. Specifically, based on the concepts of statistical linearization and of stochastic averaging, the system response amplitude is modeled as a one-dimensional Markov diffusion process. Further, using a discrete version of the Chapman-Kolmogorov equation and the associated first-order stochastic differential equation, the response amplitude and first-passage PDFs are derived. The main concept of the approach relates to the evolution of the response PDF in short time steps, assuming a Gaussian form for the conditional response PDF. A number of nonlinear oscillators are considered in the numerical examples section including the versatile Preisach hysteretic oscillator. For this oscillator, first-passage PDFs are derived for the first time to the authors’ best knowledge. Comparisons with pertinent Monte Carlo data demonstrate the reliability of the approach.
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Published In
Journal of Engineering Mechanics
Volume 139 • Issue 9 • September 2013
Pages: 1207 - 1217
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Apr 9, 2012
Accepted: Nov 2, 2012
Published online: Nov 5, 2012
Published in print: Sep 1, 2013
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