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Response and First-Passage Statistics of Nonlinear Oscillators via a Numerical Path Integral Approach
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.
Response and First-Passage Statistics of Nonlinear Oscillators via a Numerical Path Integral Approach
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.
Response and First-Passage Statistics of Nonlinear Oscillators via a Numerical Path Integral Approach
Kougioumtzoglou, Ioannis A. (author) / Spanos, Pol D. (author)
Journal of Engineering Mechanics ; 139 ; 1207-1217
2012-11-05
112013-01-01 pages
Article (Journal)
Electronic Resource
English
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