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Thermally generated transient frequency excursions in doubly‐rotated quartz thickness‐mode resonators

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2 Author(s)
Sinha, B.K. ; Schlumberger‐Doll Research, Ridgefield, Connecticut 06877 ; Tiersten, H.F.

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The temperature distribution in the electroded quartz plate is obtained from the uncoupled heat conduction equation subject to appropriate initial and boundary conditions. The time‐dependent biasing state resulting from the transient temperature distribution is determined from the exact equations of static linear thermoelasticity for electrode films of zero thickness and from a system of approximate thermoelastic extensional plate equations for electrode films of finite thickness. The time‐dependent change in resonant frequency resulting from the biasing state is determined from an equation for the perturbation of the eigenfrequency due to a bias. Results are presented for a number of thermally compensated as well as uncompensated cuts of quartz for some physically meaningful temperature inputs. In particular the calculations show that in thermally compensated cuts with electrodes of finite thickness, the frequency initially shifts considerably beyond the equilibrium resonant frequency for the final uniform temperature state.

Published in:

Journal of Applied Physics  (Volume:55 ,  Issue: 9 )

Date of Publication:

May 1984

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