Prediction of Natural Frequencies for In-plane Vibration Modes of Circular Ring with Rectangular Cross Section

Abstract

This study presentsan advanced mathematical model for predicting the in-plane natural frequencies of circular rings with rectangular cross-sections, a critical factor in vibration control. Building on Hoppe’s predictive formula for in-plane vibrations of rings, which has been extensively applied in fields such as mechanical and structural engineering, the proposed model integrates curved beam theory with experimental validation to enhance accuracy. The research compares the proposed model with conventional methods designed for thin-walled and thick-walled rings. Relative errors between theoretical predictions and FEM simulations are quantified. For both thin-walled and thick-walled rings, relative errors in natural frequency predictions increase as the mode number and the ratio of wall thickness to ring radius increase. Across different mode numbers and thickness-to-radius ratios, the conventional methods exhibited relative errors of 10% to 40%, depending on the specific parameters. The proposed model, based on curved beam theory, demonstrated an improvement in accuracy, predicting in-plane natural frequencies with a relative error of approximately 5% for a wall thickness of about 20% of the metal ring’s radius. This advancement provides a more reliable method for predicting the in-plane vibrations of circular rings, crucial for addressing engineering challenges across multiple disciplines.