Role of depth and location of minima of a double-well potential on vibrational resonance

We report our investigation into the role of depth and location of minima of a double-well potential on vibrational resonance in both underdamped and overdamped Duffing oscillators. The systems are driven by both low- and high-frequency periodic forces. We obtain theoretical expressions for the amplitude g of the high-frequency force at which resonances occur. The depth and location of the minima of the potential wells have a distinct effect on vibrational resonance in the underdamped and overdamped cases. In the underdamped system at least one resonance and at most two resonances occur and the number of resonances can be altered by varying the depth and location of the minima of the potential wells. We show that in the overdamped system there is always one and only one resonance, and the value of g at which resonance occurs is independent of the depth of the wells, but varies linearly with the locations of the minima of the wells.