December 24, 2018 14:49 WSPC/S0218-1274 1850170
Vibro-Impact Viscoelastic Oscil lator with Fractional Derivative Element
the same analysis, stochastic bifurcation takes place
as fractional derivative order αincreases from 0.1
We discussed the stochastic bifurcation of a vibro-
impact oscillator with fractional derivative element
and a viscoelastic term under Gaussian white noise
excitation. The original oscillator is converted to
an equivalent oscillator without a viscoelastic term.
The stochastic averaging method and the nons-
mooth transformation are utilized to obtain the
analytical solutions the eﬀectiveness of which can
be veriﬁed by numerical solutions. We also discussed
the stochastic bifurcation phenomenon induced by
the viscoelastic parameters, fractional coeﬃcient
and fractional derivative order.
This work is supported by the National Natural Sci-
ence Foundation of China (NSFC) under the Grant
Nos. 11472212, 11532011 and by Shaanxi Natural
Science Foundation of China under the Grant No.
2017JM1038. The ﬁrst author (Y.-G. Yang) would
like to thank the China Scholarship Council (No.
201606290189) and the hospitality of University of
California, Merced, during his visit from August
2016 to August 2018.
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