Surface vibrational modes in disk-shaped resonators.

Area of Science:

• Solid Mechanics
• Acoustics
• Materials Science

Background:

• Understanding vibrational modes in elastic disks is crucial for applications in acoustics and mechanical engineering.
• Previous studies have explored various vibrational modes, but specific focus on low-lying resonant vibrations with large angular wave numbers in thin disks is less common.

Purpose of the Study:

• To calculate natural frequencies and displacement distributions for surface vibrational modes in thin isotropic elastic disks.
• To investigate even solutions for low-lying resonant vibrations with large angular wave numbers.
• To compare theoretical calculations with experimental measurements for validation.

Main Methods:

• Theoretical calculation of natural frequencies and displacement components for vibrational modes.
• Experimental modal analysis using resonant excitation on a duralumin disk (radius ≈90 mm, thickness 16 mm).
• Frequency range of 130-200 kHz for experimental measurements.

Main Results:

• Identified several families of modes, interpreted as modified cylinder surface modes and plate Lamb modes.
• Achieved excellent agreement between calculated and experimentally measured frequencies.
• Observed splitting in resonant peaks for approximately half of the measured modes (Δfsplit/fmode ~ 10⁻⁵).
• Measured high Q-factors (2–3×10⁵) for all modes in vacuum, typical for duralumin resonators.

Conclusions:

• The theoretical model accurately predicts the vibrational modes and frequencies of thin elastic disks.
• The observed mode splitting and high Q-factors provide insights into the behavior of mechanical resonators in the ultrasonic range.
• The findings are relevant for designing and optimizing ultrasonic devices and acoustic systems.