Nonlinear contact mechanics based on ring-down experiments with quartz crystal resonators

We report on the explicit derivation of a nonlinear spring constant and a nonlinear friction coefficient describing the interaction between an oscillating quartz plate and a tip touching its surface. The analysis is based on ring-down experiments. After the electrical excitation is turned off, the decay of the oscillation shows an amplitude-dependent resonance frequency and decay rate. This "chirp" does not occur when the quartz plate is out of contact. The chirp and the nonlinear decay rate are converted to a nonlinear spring constant kappa(1)(x) and a nonlinear friction coefficient xi(1)(x) by means of a perturbation analysis. (C) 2003 American Institute of Physics.