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Study of the bending modes in circular quartz resonators
Philippe Leclaire1, Jozefien Goossens, Loïc Martinez
1Laboratorium voor Akoestiek en Thermische Fysica, Katholieke Universiteit Leuven, B-3001 Heverlee, Belgium. Philippe.Leclaire@fys.kuleuven.be
Summary
This study investigates bending modes in piezoelectric quartz disks, finding good agreement between experimental and theoretical results for resonance frequencies and mode shapes at lower frequencies. Anisotropy was observed at higher frequencies, not predicted by the classical model.
Area of Science:
- Materials Science
- Solid Mechanics
- Acoustics
Background:
- Piezoelectric materials like quartz exhibit complex mechanical behaviors under electrical excitation.
- Understanding bending modes is crucial for applications involving resonators and sensors.
Purpose of the Study:
- To experimentally and theoretically investigate bending modes in a partially electroded circular AT-cut quartz disk.
- To compare experimental results with classical thin disk bending theory and Lamb wave theory.
Main Methods:
- Excitation of the quartz disk using a voltage pulse applied to electrodes.
- Measurement of out-of-plane displacements via laser vibrometry.
- Application of classical thin disk bending theory for analysis.
Main Results:
- Good agreement between experimental and theoretical resonance frequencies and forced mode shapes at frequencies below 6 MHz.
- Observed anisotropy at higher frequencies, not accounted for by the classical model.
- Experimental phase velocities correlate with the classical theory of disks and the Lamb A(0) mode.
Conclusions:
- Confirms the correspondence between the Lamb A(0) mode and bending eigenmodes of finite-sized quartz disks at low frequencies.
- Highlights limitations of classical models in predicting higher-frequency behavior and anisotropy.
- Suggests that mounting springs introduce additional clamping effects impacting results.
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