Modulating Friction by the Phase of the Vertical Vibrational Excitation at Washboard Frequency

Applying external vibrations at the resonant frequencies of the frictional system has been a highly effective approach to suppress friction but usually requires additional energy consumption. In this study, we find that in addition to exerting the vibration at the resonant frequency of the frictional system, the friction force on the atomically flat silicon surface can also present a local minimum when the oscillation frequency of the vertical vibrational excitation equals the washboard frequency with respect to the sliding velocity. Moreover, compared with the additional energy consumption at the resonant frequency, applying vertical vibrational excitation at the washboard frequency requires much less energy consumption. The study further shows that the friction force under the washboard frequency can be effectively mediated depending on how the initial phase angle of the vertical vibrational excitation affects the effective substrate potential barrier at the slip moment of the tip. We have also extended the proposed friction modulation technique on atomically flat surfaces to periodic textured surfaces and confirmed its practicality and great potential for controlling friction.