Dynamics of a Duffing oscillator with two time delays in feedback control under narrow-band random excitation

The paper presents analytical and numerical results of the primary resonance of a Duffing oscillator with two distinct time delays in the linear feedback control under narrowband random excitation. Using the method of multiple scales, the first-order and the second-order steady-state moments of the primary resonance are derived. For the case of two distinct time delays, the appropriate choices of the combinations of the feedback gains and the difference between two time delays are discussed from the viewpoint of vibration control and stability. The analytical results are in well agreement with the numerical results.