Nonlinearities in contact mechanics experiments with quartz crystal resonators

The nonlinear forces acting at the surface of an oscillating quartz crystal, which is in contact with a tip, were studied using the “ring-down” method. The resonator is excited at its resonance frequency and then decays freely after the AC driving voltage is turned off. The voltage across the electrodes during the decay is proportional to the time-dependent shear strain inside the plate. Non-sinusoidal components of the oscillation are directly visualized. For statistical analysis we mostly rely on the amplitudes of anharmonic overtones as determined with a Fourier analysis. These amplitudes display a maximum when the tip just barely touches the oscillating surface. Even overtones indicate the presence of normal forces. The occurrence of these normal stresses is attributed to adhesion hysteresis in the rim of the contact area.