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.

本文通过具有分数阻尼项来处理具有记忆的非理想系统。该系统的特征是附加的三次非线性。基于该非理想模型数值模拟的时间序列形式，研究了系统的非线性动力响应。由不平衡的旋转质量驱动的具有受限电源的直流电动机提供了不理想的激励。为了区分周期性和非周期性行为，他们使用了三种不同的数学工具，即0-1测试，比例指数和小波技术。相对于分数阻尼导数项和直流电动机中施加的电压（作为控制参数），研究了所考虑系统的响应。数值结果表明，比例指数，