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Numerical Solution of the Four-Dimensional Nonstationary Fokker-Planck Equation

  • S. F. Wojtkiewicz
  • L. A. Bergman
  • B. F. Spencer
  • E. A. Johnson
Part of the Solid Mechanics and its Applications book series (SMIA, volume 85)

Abstract

The response of mechanical and structural systems subjected to environmental loads is often determined through the use of random vibration methods. Many of these loads can be effectively modeled as random processes, and more specifically as Gaussian white noise or filtered Gaussian white noise excitations. This choice of excitation model infers that the response of the system will be Markovian and, thus, expressible in terms of its transition probability density function, which satisfies both the forward (Fokker-Planck) and backward Kolmogorov equations.

Keywords

Iterative Solver Kolmogorov Equation Temporal Discretization White Noise Excitation High Order Finite Difference 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • S. F. Wojtkiewicz
    • 1
  • L. A. Bergman
    • 2
  • B. F. Spencer
    • 3
  • E. A. Johnson
    • 4
  1. 1.Department of Aeronautical and Astronautical EngineeringUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  2. 2.Department of Aeronautical and Astronautical EngineeringUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  3. 3.Department of Civil Engineering and Geological SciencesUniversity of Notre DameNotre DameUSA
  4. 4.Department of Civil Engineering and Geological SciencesUniversity of Notre DameNotre DameUSA

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