Jump threshold in a forced and time-delayed Hertzian contact oscillator near the 2-subharmonic resonances

In this problem we analyze the influence of external feedback time on the threshold in a forced nonlinear Hertzian contact system nearby the sub-harmonic resonance. A perturbation method is performed to approximate vibration amplitudes and their stability near the secondary resonance. The influence of delay state feedback presents in the posi-tion, in the velocity or in both cases are studied. The analytical results shown that for appropriate values of the gain and time delay, the fre-quency amplitudes shift in the direction of high or low frequencies where the softening bistability persists.