TY - JOUR
T1 - Bifurcation Analysis of a Vibro-Impact Viscoelastic Oscillator with Fractional Derivative Element
AU - Yang, Yong Ge
AU - Xu, Wei
AU - Chen, Yang Quan
AU - Zhou, Bingchang
N1 - Publisher Copyright:
© 2018 World Scientific Publishing Company.
PY - 2018/12/30
Y1 - 2018/12/30
N2 - To the best of authors' knowledge, little work has been focused on the noisy vibro-impact systems with fractional derivative element. In this paper, stochastic bifurcation of a vibro-impact oscillator with fractional derivative element and a viscoelastic term under Gaussian white noise excitation is investigated. First, the viscoelastic force is approximately replaced by damping force and stiffness force. Thus the original oscillator is converted to an equivalent oscillator without a viscoelastic term. Second, the nonsmooth transformation is introduced to remove the discontinuity of the vibro-impact oscillator. Third, the stochastic averaging method is utilized to obtain analytical solutions of which the effectiveness can be verified by numerical solutions. We also find that the viscoelastic parameters, fractional coefficient and fractional derivative order can induce stochastic bifurcation.
AB - To the best of authors' knowledge, little work has been focused on the noisy vibro-impact systems with fractional derivative element. In this paper, stochastic bifurcation of a vibro-impact oscillator with fractional derivative element and a viscoelastic term under Gaussian white noise excitation is investigated. First, the viscoelastic force is approximately replaced by damping force and stiffness force. Thus the original oscillator is converted to an equivalent oscillator without a viscoelastic term. Second, the nonsmooth transformation is introduced to remove the discontinuity of the vibro-impact oscillator. Third, the stochastic averaging method is utilized to obtain analytical solutions of which the effectiveness can be verified by numerical solutions. We also find that the viscoelastic parameters, fractional coefficient and fractional derivative order can induce stochastic bifurcation.
KW - fractional derivative element
KW - Stochastic bifurcation
KW - vibro-impact
KW - viscoelastic oscillator
UR - http://www.scopus.com/inward/record.url?scp=85059743080&partnerID=8YFLogxK
U2 - 10.1142/S0218127418501705
DO - 10.1142/S0218127418501705
M3 - 文章
AN - SCOPUS:85059743080
SN - 0218-1274
VL - 28
JO - International Journal of Bifurcation and Chaos
JF - International Journal of Bifurcation and Chaos
IS - 14
M1 - 18501705
ER -