Simulating Frequency Nonlinearities in Quartz Resonators at High Temperature and Pressure

A. Beerwinkle[1], R. Singh[1], and G. Kirikera[2]
[1]Mechanics of Advanced Materials Laboratory, School of Mechanical and Aerospace Engineering, Oklahoma State University, Tulsa, OK
[2]Geophysical Research Company, LLC, (GRC) Tulsa, OK
Published in 2011

A three-dimensional finite element model, based on the linear field equations for superimposed small vibrations onto nonlinear thermoelastic stressed media given by Lee and Yong, was developed. This method involves solving the thermal stress and piezoelectric model with geometric and material nonlinearities.

The thickness-shear mode frequency response of the model was benchmarked to experimental transducer data with temperature ranging from 50°C to 200°C and pressure from 14 psi to 20,000 psi.