Abstract In the previous parts, random vibration of linear dynamic systems are discussed. In general, spacecraft structures are considered to behave linearly and the modal characteristics play an important role in the design and verification process. In this part, random vibrations of nonlinear dynamic systems where modal properties do not exist will be briefly discussed. Many solution methods exist to solve nonlinear systems exposed to random loads. In Manohar (Sādhanā (India), 20(2–4), pages 521–526, 1995) an overview of several solution methods is given. In this chapter one particular method based on the Fokker-Planck-Kolmogorov (FPK) equation is applied to predict the response characteristics. Wang and Uhlenbeck’s paper entitled: “On the Theory of the Brownian Motion II”, published in Wax (Selected Papers on Noise and Stochastic Processes, Dover, New York, 1964) was the starting point to study the derivation and applications of the FPK equation. This paper was originally published in Reviews of Modern Physics in 1945. Caughey (J. Acoust. Soc. Am. 35(11), pages 1683–1692, 1963) repeated and extended the derivation of the FPK equation for a Markoff vector process and showed the steady state solution of the FPK equation for the nonlinear Duffing equation with a Gaussian white noise load. Risken’s book (Risken in The Fokker-Planck Equation, Methods of Solution and Applications, Springer, Berlin, 1989), is completely dedicated to the FPK equation, methods of solution and applications, however, it has little to do with the mechanical engineering problems. Ibrahim (Parametric Random Vibration, Dover, New York, 1985) describes in his book the parametric random vibrations and Roberts and Spanos (Random Vibration and Statistical Linearization, Dover, New York, 1999) discuss in their book the solution of random vibrations of nonlinear dynamic systems using statistical linearization. To’s book (To in Nonlinear Random Vibration, Analytical Techniques and Applications, Swets & Zeitlinger, Lisse, 2000) is more or less an union of the topics described in Ibrahim (Parametric Random Vibration, Dover, New York, 1985), Roberts and Spanos (Random Vibration and Statistical Linearization, Dover, New York, 1999).
Fokker-Planck-Kolmogorov Method or Diffusion Equation Method
Random Vibrations in Spacecraft Structures Design ; 5 ; 323-403
Solid Mechanics and Its Applications ; 165 , 5
2009-01-01
81 pages
Aufsatz/Kapitel (Buch)
Elektronische Ressource
Englisch
CONJUGATE UNSCENTED TRANSFORM-BASED APPROACH TO SOLVE THE FOKKER-PLANCK-KOLMOGOROV EQUATION
British Library Conference Proceedings | 2016
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