TY - JOUR
T1 - Stochastic bifurcations in the nonlinear vibroimpact system with fractional derivative under random excitation
AU - Yang, Yongge
AU - Xu, Wei
AU - Sun, Yahui
AU - Xiao, Yanwen
N1 - Publisher Copyright:
© 2016 Elsevier B.V.
PY - 2017/1/1
Y1 - 2017/1/1
N2 - This paper aims to investigate the stochastic bifurcations in the nonlinear vibroimpact system with fractional derivative under random excitation. Firstly, the original stochastic vibroimpact system with fractional derivative is transformed into equivalent stochastic vibroimpact system without fractional derivative. Then, the non-smooth transformation and stochastic averaging method are used to obtain the analytical solutions of the equivalent stochastic system. At last, in order to verify the effectiveness of the above mentioned approach, the van der Pol vibroimpact system with fractional derivative is worked out in detail. A very satisfactory agreement can be found between the analytical results and the numerical results. An interesting phenomenon we found in this paper is that the fractional order and fractional coefficient of the stochastic van der Pol vibroimpact system can induce the occurrence of stochastic P-bifurcation. To the best of authors' knowledge, the stochastic P-bifurcation phenomena induced by fractional order and fractional coefficient have not been found in the present available literature which studies the dynamical behaviors of stochastic system with fractional derivative under Gaussian white noise excitation.
AB - This paper aims to investigate the stochastic bifurcations in the nonlinear vibroimpact system with fractional derivative under random excitation. Firstly, the original stochastic vibroimpact system with fractional derivative is transformed into equivalent stochastic vibroimpact system without fractional derivative. Then, the non-smooth transformation and stochastic averaging method are used to obtain the analytical solutions of the equivalent stochastic system. At last, in order to verify the effectiveness of the above mentioned approach, the van der Pol vibroimpact system with fractional derivative is worked out in detail. A very satisfactory agreement can be found between the analytical results and the numerical results. An interesting phenomenon we found in this paper is that the fractional order and fractional coefficient of the stochastic van der Pol vibroimpact system can induce the occurrence of stochastic P-bifurcation. To the best of authors' knowledge, the stochastic P-bifurcation phenomena induced by fractional order and fractional coefficient have not been found in the present available literature which studies the dynamical behaviors of stochastic system with fractional derivative under Gaussian white noise excitation.
KW - Fractional derivative
KW - Non-smooth transformation
KW - Stochastic averaging method
KW - Stochastic bifurcation
KW - Van der Pol
KW - Vibroimpact systems
UR - http://www.scopus.com/inward/record.url?scp=84971283882&partnerID=8YFLogxK
U2 - 10.1016/j.cnsns.2016.05.004
DO - 10.1016/j.cnsns.2016.05.004
M3 - 文章
AN - SCOPUS:84971283882
SN - 1007-5704
VL - 42
SP - 62
EP - 72
JO - Communications in Nonlinear Science and Numerical Simulation
JF - Communications in Nonlinear Science and Numerical Simulation
ER -