Stochastic Bifurcation of a Strongly Non-Linear Vibro-Impact System with Coulomb Friction under Real Noise
Abstract
:1. Introduction
1.1. Background
1.2. Literature Survey
1.3. Formulation of the Problem
1.4. Contribution of this Study
1.5. Organization
2. System Description and Non-Smooth Transformation
2.1. System Description
2.2. Non-Smooth Transformation
3. Stochastic Averaging Procedure
4. Response Probability Density Functions
5. Example
5.1. The Effect of System Parameters on Response
5.2. Stochastic Bifurcations
6. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
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Liu, L.; Xu, W.; Yue, X.; Huang, D. Stochastic Bifurcation of a Strongly Non-Linear Vibro-Impact System with Coulomb Friction under Real Noise. Symmetry 2019, 11, 4. https://doi.org/10.3390/sym11010004
Liu L, Xu W, Yue X, Huang D. Stochastic Bifurcation of a Strongly Non-Linear Vibro-Impact System with Coulomb Friction under Real Noise. Symmetry. 2019; 11(1):4. https://doi.org/10.3390/sym11010004
Chicago/Turabian StyleLiu, Li, Wei Xu, Xiaole Yue, and Dongmei Huang. 2019. "Stochastic Bifurcation of a Strongly Non-Linear Vibro-Impact System with Coulomb Friction under Real Noise" Symmetry 11, no. 1: 4. https://doi.org/10.3390/sym11010004
APA StyleLiu, L., Xu, W., Yue, X., & Huang, D. (2019). Stochastic Bifurcation of a Strongly Non-Linear Vibro-Impact System with Coulomb Friction under Real Noise. Symmetry, 11(1), 4. https://doi.org/10.3390/sym11010004