Stochastic P-Bifurcation of a Bistable Viscoelastic Beam with Fractional Constitutive Relation under Gaussian White Noise
Joint Authors
Wu, Zhiqiang
Li, Yajie
Zhang, Guoqi
Wang, Feng
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-12-02
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
In this paper, we study the stochastic P-bifurcation problem for axially moving of a bistable viscoelastic beam with fractional derivatives of high order nonlinear terms under Gaussian white noise excitation.
First, using the principle for minimum mean square error, we show that the fractional derivative term is equivalent to a linear combination of the damping force and restoring force, so that the original system can be simplified to an equivalent system.
Second, we obtain the stationary Probability Density Function (PDF) of the system’s amplitude by stochastic averaging, and using singularity theory, we find the critical parametric condition for stochastic P-bifurcation of amplitude of the system.
Finally, we analyze the types of the stationary PDF curves of the system qualitatively by choosing parameters corresponding to each region within the transition set curve.
We verify the theoretical analysis and calculation of the transition set by showing the consistency of the numerical results obtained by Monte Carlo simulation with the analytical results.
The method used in this paper directly guides the design of the fractional order viscoelastic material model to adjust the response of the system.
American Psychological Association (APA)
Li, Yajie& Wu, Zhiqiang& Zhang, Guoqi& Wang, Feng. 2018. Stochastic P-Bifurcation of a Bistable Viscoelastic Beam with Fractional Constitutive Relation under Gaussian White Noise. Discrete Dynamics in Nature and Society،Vol. 2018, no. 2018, pp.1-10.
https://search.emarefa.net/detail/BIM-1152751
Modern Language Association (MLA)
Li, Yajie…[et al.]. Stochastic P-Bifurcation of a Bistable Viscoelastic Beam with Fractional Constitutive Relation under Gaussian White Noise. Discrete Dynamics in Nature and Society No. 2018 (2018), pp.1-10.
https://search.emarefa.net/detail/BIM-1152751
American Medical Association (AMA)
Li, Yajie& Wu, Zhiqiang& Zhang, Guoqi& Wang, Feng. Stochastic P-Bifurcation of a Bistable Viscoelastic Beam with Fractional Constitutive Relation under Gaussian White Noise. Discrete Dynamics in Nature and Society. 2018. Vol. 2018, no. 2018, pp.1-10.
https://search.emarefa.net/detail/BIM-1152751
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1152751