Off-resonance Cantilever Dynamics in the Presence of Attractive and Repulsive Tip Interaction Forces

In dynamic atomic force microscopy (AFM), as the tip of the base-excited micro-cantilever approaches the sample surface, this cantilever tip typically experiences long-range attractive and short_range repulsive forces. Due to the strongly nonlinear nature of these tip-sample interaction forces, various nonlinear phenomena including grazing contact-related phenomena have been observed. With the aim of obtaining a better understanding of such phenomena, a macro-scale experimental system has been constructed with attractive and repulsive tip interactions. In this arrangement, the macro-scale cantilever structure is harmonically excited at its base, a combination of magnets is used to generate the attractive forces, and impacts with a compliant surface are used to produce the repulsive forces. The separation between the tip and the compliant surface is used as a control parameter and the associated qualitative changes in the system dynamics are studied on Poincaré sections constructed by using the excitation frequency as the clock frequency. Off-resonance excitations are considered and a period- doubling window is observed for near-grazing impacts when the excitation frequency is in between the first and the second natural frequencies of the system. To explore the experimental observations further, a reduced-order model of the macro-scale system is developed with Derjaguin–Muller–Toporov (DMT) contact mechanics. The dynamics of the reduced-order system is found to agree well with the corresponding experimental observations. The nonlinear phenomenon observed during off-resonance excitations can form a basis for engineering grazing (zero-speed) impacts or low-speed impacts between a tapping mode AFM cantilever tip and the considered sample. In addition, the macro-scale experimental arrangement can serve as a vehicle to understand the dynamics of elastic structures subjected to different combinations of attractive and repulsive tip forces.