International Journal of Applied Electromagnetics and Mechanics 22 (2005) 69–82 69 IOS Press Application of a DC-bias to reduce acceleration sensitivity in quartz resonators Yook-Kong Yong ∗ and Mihir S. Patel Civil and Environmental Engineering, Rutgers University, Piscataway, NJ 08854, USA Abstract. A quartz resonator subjected to acceleration will deform due to inertial effects. The deformation stresses and strains in the plate will in turn cause a shift in the resonator frequencies. A method is proposed to actively minimize the inertial stresses and strains by a DC-bias electric field. Finite element models are created to calculate the effects of acceleration on resonant frequency and to compare the results with experimental data. The non-linearity and non-homogeneity induced by the inertial forces are modeled by using the concept of a superposed state. The model results for the acceleration effects are shown to compare well with the experimental results. The models are then used to calculate the effects of a DC electric field bias and to demonstrate the reduction of acceleration sensitivity. 1. Introduction The origin of some frequency instabilities in quartz resonators are due to the nonlinear behavior of quartz. The nonlinearities lead to two different phenomena, which correspond to either (a) propagation of finite amplitude waves in a nonlinear medium or (b) the propagation of a small amplitude wave in the nonlinear strained medium [1]. A good example of phenomenon (b) is the nonlinear coupling between a thickness shear mode and a quasi-static deformation due to either temperature, force, pressure, or acceleration. When a piezoelectric crystal resonator is subjected to very low frequency vibrations or accelerations, stresses and strains in the crystal are induced by the inertial forces. The stresses and strains are quasi-static with respect to a much higher frequency thickness shear mode. The material nonlinearities couple these quasi-static stresses and strains to the high frequency thickness shear wave, which in turn changes its thickness shear frequency. In an anisotropic medium, the nonlinear effects depend on the crystal orientation and on the wave propagation direction. Particular configurations can be found with minimized acceleration sensitivities for a resonator. One could also counteract the effect of acceleration by a DC bias. In the present paper, finite element models are developedboth for AT- and SC-cut crystals by using the basic equations of the theory of small deformations superposed on finite initial deformations derived in a Lagrangian formulation. Force-frequency simulations are carried out and then the model is stiffened by the application of a DC-bias. The application of a DC-bias proves that the force frequency effect can be counteracted by applying a DC bias in the opposite direction and equal magnitude. ∗ Corresponding author. E-mail: yyong@rci.rutgers.edu. 1383-5416/05/$17.00 © 2005 – IOS Press and the authors. All rights reserved