Dynamic response of mechanical systems to impulse process stochastic excitations: Markov approach

5th Symposium on the Mechanics of Slender Structures

物理学;力学

Iwankiewicz, R.^1,2

Hamburg University of Technology, Eissendorfer Strasse 42, Hamburg

21073, Germany^1

University of Zielona Gora, ul. Prof. Szafrana 1, Zielona Gora

65-516, Poland^2

关键词: Chapman-Kolmogorov equation;    Diffusive Markov process;    Mechanical dynamics;    Mechanical systems;    Moment equations;    Poisson impulse;    Probability densities;    Stochastic excitations;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/721/1/012010/pdf
DOI  :  10.1088/1742-6596/721/1/012010

学科分类：力学，机械学

来源: IOP

【 摘 要 】

Methods for determination of the response of mechanical dynamic systems to Poisson and non-Poisson impulse process stochastic excitations are presented. Stochastic differential and integro-differential equations of motion are introduced. For systems driven by Poisson impulse process the tools of the theory of non-diffusive Markov processes are used. These are: the generalized Itô's differential rule which allows to derive the differential equations for response moments and the forward integro-differential Chapman-Kolmogorov equation from which the equation governing the probability density of the response is obtained. The relation of Poisson impulse process problems to the theory of diffusive Markov processes is given. For systems driven by a class of non-Poisson (Erlang renewal) impulse processes an exact conversion of the original non-Markov problem into a Markov one is based on the appended Markov chain corresponding to the introduced auxiliary pure jump stochastic process. The derivation of the set of integro-differential equations for response probability density and also a moment equations technique are based on the forward integro-differential Chapman-Kolmogorov equation. An illustrating numerical example is also included.