| Summary: | In this work, we consider a fractional nonlinear
vibration system of Duffing type with harmonic excitation
by using the fractional derivative operator -∞−1Dαt and the
averaging method. We derive the steady-state periodic response
and the amplitude-frequency and phase-frequency
relations. Jumping phenomena caused by the nonlinear
term and resonance peaks are displayed, which is similar
to the integer-order case. It is possible that a minimum
of the amplitude exists before the resonance appears for
some values of the modelling parameters, which is a feature
for the fractional case. The effects of the parameters in
the fractional derivative term on the amplitude-frequency
curve are discussed.
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