Exact Stationary-Response Solution for Second Order Nonlinear Systems Under Parametric and External White-Noise Excitations

DOI10.1115/1.3173029zbMath0613.73085OpenAlexW2109219092MaRDI QIDQ4720906

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Publication date: 1987

Published in: Journal of Applied Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1115/1.3173029

zbMATH Keywords

nonlinear systems stationary solutions Gaussian white noises microscopic reversibility parametric random excitations external random excitations method of detailed balance reduced Fokker-Planck equations

Mathematics Subject Classification ID

Random vibrations in mechanics of particles and systems (70L05) Random vibrations in dynamical problems in solid mechanics (74H50)

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Nonstationary probability densities of strongly nonlinear single-degree-of-freedom oscillators with time delay ⋮ Exact and approximate response of non-linear stochastic systems ⋮ Probabilistic response of nonsmooth nonlinear systems under Gaussian white noise excitations ⋮ Stochastic modeling of nonlinear oscillators under combined Gaussian and Poisson white noise: a viewpoint based on the energy conservation law ⋮ The closed-form solution of the reduced Fokker-Planck-Kolmogorov equation for nonlinear systems ⋮ Stochastic differential calculus for Gaussian and non-Gaussian noises: a critical review ⋮ Exact solutions for stationary responses of several classes of nonlinear systems to parametric and/or external white noise excitations ⋮ Methods of nonlinear random vibration analysis. ⋮ Exact stationary solutions independent of energy for strongly nonlinear stochastic systems of multiple degrees of freedom

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