Dynamics and control of periodic and non-periodic behavior of Duffing vibrating system with fractional damping and excited by a non-ideal motor

This paper deals with a non-ideal system with memory by possessing a fractional damping term. The system is characterized by additional cubic nonlinearity. Based on the time series form of the numerical simulations of this non-ideal model, the nonlinear dynamical response of the system is investigated. A DC electric motor with limited power supply driving by an unbalanced rotating mass provides the non-ideal excitation. To distinguish between periodic and non-periodic behaviors, they are used three different mathematical tools, which are the 0–1 test, scale index and wavelet technique. The response of the considered system is investigated with respect to the fractional damping derivative term and the voltage applied in the DC motor, which is considered as a control parameter. Numerical results showed that, the scale index, 0–1 test and the wavelet transform technique defined very accurately the periodic and non-periodic motions.