Nonlinear Effects of Initial Bending on the Vibrations of Crystal Plates.
Abstract
The changes in the resonance frequencies of circular crystal plates subject to initial bending stresses are studied. The plate is flexed as a cantilever clamped near the edge and stressed by a transverse, concentrated force applied at a point diametrically opposite the support. A system of plate equations which takes into account the nonlinear effects due to the large, initial deflection and to the third-order elastic stiffness coefficients in the stress-strain relations is employed. In obtaining the initial fields caused by bending, strain components are assumed to be small, but large gradient of plate deflection and large rotations of the plate element about x sub 1 and x sub 3 axes are permissible by retaining their quadratic terms in the strain-displacement relations. The changes of resonance frequencies of fundamental thickness-shear vibrations are calculated for rotation Y-cuts of quartz piezoelectric crystals. The calculated frequency changes are compared with experimental values as a function of the magnitude of the position, the azimuth angle psi, and also as a function of the magnitude of the force P.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1974
- Accession Number
- ADA006648
Entities
People
- P. C. Y. Lee
- X. Markenscoff
- Y. S. Wang
Organizations
- Princeton University