Vibration of a Rotating Micro-Ring under Electrical Field Based on Inextensible Approximation.

Area of Science:

• Mechanical Engineering
• Vibrational Dynamics
• Electromechanical Systems

Background:

• Vibrations of rotating rings are critical in engineering applications like vibratory ring gyroscopes.
• Electrostatic actuation and sensing in these gyroscopes involve complex non-linear electromechanical coupling.
• Existing analytical models for electrostatic microstructures are often complicated.

Purpose of the Study:

• To present the first analytical model for the free vibration of a rotating ring under a uniform electrical field.
• To provide insights for designing vibratory ring gyroscopes.
• To explore potential new engineering applications.

Main Methods:

• An analytical model based on thin-ring theory was derived using the energy method.
• Closed-form solutions for natural frequencies and modes were obtained via modal expansion.
• The model analyzes the effects of uniform electrical fields on rotating rings.

Main Results:

• An electrical field introduces an electrostatic force and an equivalent negative electrical-stiffness.
• This negative stiffness lowers the natural frequencies and critical speeds of the rotating ring.
• Electrical fields reduce the speeds at which rings buckle and decrease traveling mode velocities.

Conclusions:

• The study provides valuable insights into the vibration dynamics of rotating rings under electrical fields.
• The findings are directly applicable to improving the design and performance of vibratory ring gyroscopes.
• The research opens avenues for novel engineering applications leveraging these electromechanical effects.