One-dimensional equations for a piezoelectric ring and applications in a gyroscope

Area of Science:

• Solid Mechanics
• Piezoelectric Materials
• Vibrational Analysis

Background:

• Piezoelectric materials enable electromechanical coupling, crucial for sensor applications.
• Vibrational analysis of thin structures like rings is essential for micro-electromechanical systems (MEMS) design.
• Ring gyroscopes offer unique advantages in inertial sensing due to their geometry.

Purpose of the Study:

• To derive one-dimensional equations for coupled extensional and flexural vibrations in a piezoelectric ring.
• To analyze the performance of a ring piezoelectric gyroscope using these derived equations.
• To investigate the influence of rotation rate and other parameters on resonant frequencies and voltage sensitivity.

Main Methods:

• Derivation of one-dimensional equations governing coupled in-plane extensional and flexural vibrations.
• Development of analytical solutions for free and forced vibration scenarios.
• Parametric study to evaluate the impact of rotation rate on gyroscope characteristics.

Main Results:

• Established governing equations for piezoelectric ring dynamics.
• Obtained solutions for free and forced vibrations, characterizing system response.
• Quantified the dependence of resonant frequencies and voltage sensitivity on rotation rate.

Conclusions:

• The derived equations accurately model piezoelectric ring gyroscope behavior.
• Rotation rate significantly affects resonant frequencies and voltage sensitivity.
• The study provides a foundation for optimizing piezoelectric ring gyroscope design and performance.