Chapter
Jul 7, 2014
Stochastic Responses of Duffing-Van Der Pol Vibro-Impact Oscillator with Colored Noise
Authors: Wei Xu [email protected], Chao Li [email protected], and Liang Wang [email protected]Author Affiliations
Publication: Vulnerability, Uncertainty, and Risk: Quantification, Mitigation, and Management
Abstract
The purpose of this work is to use the stochastic averaging method to study the response of a vibro-impact system excited by additive and multiplicative colored noises. The non-smooth transformation of state variables is used to transform the vibro-impact system to a new system without impact term. The Fourier series is applied to obtain the stationary probability density function. The validity of the analytical results is verified by the numerical simulations. Moreover, stochastic P-bifurcations are also explored.
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© 2014 American Society of Civil Engineers.
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Published online: Jul 7, 2014
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ASCE Technical Topics:
- Analysis (by type)
- Chemical additives
- Chemicals
- Chemistry
- Continuum mechanics
- Dynamics (solid mechanics)
- Engineering fundamentals
- Engineering mechanics
- Environmental engineering
- Fourier analysis
- Mathematics
- Methodology (by type)
- Models (by type)
- Motion (dynamics)
- Numerical analysis
- Numerical models
- Oscillations
- Probability
- Research methods (by type)
- Solid mechanics
- Stochastic processes
- Verification
Authors
Affiliations
Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, Shaanxi, 710072, China. E-mail: [email protected]
Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, Shaanxi, 710072, China. E-mail: [email protected]
Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, Shaanxi, 710072, China. E-mail: [email protected]
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