Affiliations: [a] Piezoelectric Device Laboratory, School of Mechanical
Engineering and Mechanics, Ningbo University, Ningbo, Zhejiang, China | [b] Department of Mechanical and Materials Engineering,
University of Nebraska-Lincoln, Lincoln, NE, USA | [c] Department of Mechanical Engineering, Aeronautical
Engineering and Mechanics, Rensselaer Polytechnic Institute, Troy, NY,
USA
Correspondence:
[*]
Corresponding author: J.S. Yang, Piezoelectric Device
Laboratory, School of Mechanical Engineering and Mechanics, Ningbo University,
Ningbo, Zhejiang 315211, China. E-mail: jyang1@unl.edu
Abstract: The equation for transversely varying thickness modes in
doubly-rotated quartz resonators is applied in the analysis of the vibrations
of contoured resonators with beveled cylindrical edges. The treatment in this
work differs from that of earlier work in that the dominant condition at the
edge of the resonator is satisfied and the approximation made earlier in the
beveled annulus is not made here where the solution is exact. A procedure for
the analytical determination of the required diameter for a good resonator is
identified and calculated results are compared with those of the earlier work.
