1. Stochastic response analysis of multi-degree-of-freedom vibro-impact system undergoing Markovian jump
- Author
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Xudong Gu, Rongchun Hu, and Zicheng Deng
- Subjects
Applied Mathematics ,Mechanical Engineering ,Response analysis ,Aerospace Engineering ,Ocean Engineering ,Type (model theory) ,Markovian jump ,Control and Systems Engineering ,Hybrid system ,Excited state ,Jump ,Statistical physics ,Electrical and Electronic Engineering ,Finite set ,Energy (signal processing) ,Mathematics - Abstract
The paper treats stationary response of a stochastically excited multi-degree-of-freedom (multi-DOF) vibro-impact system undergoing Markovian jump. The vibro-impact system with sudden abrupt changes in substructures or external excitations is modeled as a continuous-discrete Markovian jump system, which is essentially different from the traditional vibro-impact model. It is demonstrated that the random jump factors switch between a finite number of modes. This salient feature allows us to identify this type of dynamic behaviors as response of hybrid vibro-impact systems undergoing Markovian jump. Utilizing a two-step approximate technique, we can reduce the considered multi-DOF hybrid system to one-dimensional averaged Ito equation of the form of system’s total energy. The approximate analytical solution of the associated Fokker–Planck–Kolmogorov (FPK) equation of system’s energy is derived to predict the stationary response of original hybrid systems. more...
- Published
- 2020
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