Internal resonance in quartz crystal resonator and mass detection in nonlinear regime

Abstract

This paper introduces the use of nonlinear jump phenomena in the frequency response of a quartz crystal resonator for mass detection. In contrast to recent studies that exploit parametric excitation for mass detection, our device exhibits nonlinear behavior modeled by the directly forced Duffing equation. In addition, internal resonance due to modal coupling is demonstrated for sufficiently large forcing amplitudes. A system of coupled Duffing equations based on a Galerkin expansion of the von Kármán plate equations is used to model these higher order effects.