An Analysis of Nonlinear Resonance in Thickness Shear and Trapped Energy Resonators.
Abstract
Electroelastic equations containing terms up to cubic in the small mechanical displacement field, but no higher than linear in the electric variables, are applied in the analysis of nonlinear resonance in rotated Y-cut quartz oscillators. Both pure thickness-shear vibrators and essentially thickness-shear trapped energy resonators are treated. Lumped parameter representations of the solutions, which are valid in the vicinity of a resonance and relate the amplitude of the dominant mode nonlinearly to the voltage across the crystal, are presented for both the pure thickness-shear and trapped energy thickness-shear problems. In each instance the expression for the current through the crystal is determined, the influence of the external circuitry is included in the analysis and, ultimately, an expression cubic in the mode amplitude and linear in the driving voltage is obtained. The analyses hold for the fundamental and odd overtone thickness-shear modes. Nonlinear resonance curves are presented for AT-cut quartz.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1975
- Accession Number
- ADA015173
Entities
People
- Harry F. Tiersten
Organizations
- Rensselaer Polytechnic Institute