A new 2-D model of a thin annular disk using a modified assumption.

Area of Science:

• Mechanical Engineering
• Vibrational Analysis
• Acoustics

Background:

• Understanding the coupled vibration of thin annular structures is crucial for designing various mechanical and acoustic systems.
• Existing models often simplify the complex vibrational behaviors, leading to inaccuracies in predicting responses.

Purpose of the Study:

• To develop an improved two-dimensional (2-D) model for thin annular structures.
• To accurately predict the impedance spectrum and displacements considering coupled radial and thickness modes.

Main Methods:

• A modified assumption regarding coupled vibration was introduced into the 2-D model.
• Finite Element Analysis (FEA) was employed to investigate bending displacement and validate the theoretical model.

Main Results:

• The model successfully obtained the impedance spectrum and displacements in both radial and thickness directions.
• FEA confirmed that bending in the thickness direction is coupled to radial modes, forming node circles at high frequencies.
• Excellent agreement was observed between the new theoretical model and FEA results.

Conclusions:

• The improved 2-D model provides a more accurate representation of thin annular structure vibrations.
• The coupled nature of thickness and radial modes is significant, especially at higher frequencies.
• The validated model can be used for precise analysis and design in relevant engineering applications.