Pseudo-Degeneracy in Handbell Modes

TL;DR

This paper investigates how adding mass to a handbell can intentionally re-combine nearly-degenerate vibrational modes into a pseudo-degenerate state, using real-time holographic interferometry for observation.

Contribution

It demonstrates a method to achieve pseudo-degeneracy in handbell modes by strategic mass addition, a novel approach in vibrational mode control.

Findings

Modes can be shifted in position and frequency through mass addition.

A pair of modes was successfully brought into pseudo-degeneracy.

Real-time holographic interferometry effectively visualizes mode changes.

Abstract

The vibrational modes of handbells exist in nearly-degenerate pairs which have been split by nonuniformities in the bell. The possibility of intentionally re-combining a pair into pseudo-degeneracy was explored by adding mass to various locations on a C4 handbell. Depending on the location and mass added to the bell, the modes can be shifted in position and frequency as observed by a real-time holographic interferometry system. By moving and varying the added mass, one pair of modes was successfully brought into a pseudo-degeneracy.