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Resonant frequency function of thickness-shear vibrations of rectangular crystal plates
Summary
Precise resonant frequencies for thickness-shear vibrations in quartz crystal resonators are crucial. This study derives a new frequency equation for rectangular plates, showing resonance depends on aspect ratio, vital for miniaturized devices.
Area of Science:
- Physics
- Materials Science
- Electrical Engineering
Background:
- Accurate resonant frequencies of thickness-shear vibrations in quartz crystal plates are essential for resonator design.
- Miniaturization of quartz crystal resonators necessitates considering both length and width effects for precise frequency calculations.
Discussion:
- This research derives frequency and wavenumber relations from 3D wave propagation equations in finite crystal plates.
- The study satisfies boundary conditions for the dominant thickness-shear mode, yielding three wavenumber solutions and constructing a frequency equation.
Key Insights:
- The resonant frequency of the thickness-shear mode is a second-order polynomial function of aspect ratios.
- The derived frequency equation aligns with established results in its simplest form.
Outlook:
- The new frequency equation provides a foundation for further analytical and experimental investigations of quartz crystal resonators.
- This work supports the advancement of high-precision frequency control in electronic devices.
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