Exact solutions for stationary responses of several classes of nonlinear systems to parametric and/or external white noise excitations

DOI10.1007/BF02014541zbMath0748.60055OpenAlexW2026688088MaRDI QIDQ1191584

Wei-Qiu Zhu

Publication date: 27 September 1992

Published in: Applied Mathematics and Mechanics. (English Edition) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02014541

zbMATH Keywords

existence and uniquenessnonlinear stochastic systemsFokker-Planck-Kolmogorov equationstationary responses

Mathematics Subject Classification ID

Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) (60J70) Stochastic analysis (60H99)

Related Items

The closed-form solution of the reduced Fokker-Planck-Kolmogorov equation for nonlinear systems, A generalized analysis technique of the stationary FPK equation in nonlinear systems under Gaussian white noise excitations, A probabilistic decomposition-synthesis method for the quantification of rare events due to internal instabilities, Exact stationary solutions independent of energy for strongly nonlinear stochastic systems of multiple degrees of freedom

Cites Work

• The exact steady-state solution of a class of nonlinear stochastic systems
• Exact solution of a particular problem of oscillations of a system with random parametric excitation
• An exact solution to a certain nonlinear random vibration problem
• Random Vibration: A Survey of Recent Developments
• Exact Stationary-Response Solution for Second Order Nonlinear Systems Under Parametric and External White-Noise Excitations
• The Steady-State Response of a Class of Dynamical Systems to Stochastic Excitation