Tuning natural modes of vibration by prestress in the design of a harmonic gong

Abstract

Prestresses are purposefully added to an object to improve its performance, such as tuning a guitar string by adding tension. This paper reports how the normal modes of a sheet metal component can be tuned through the prestresses generated by cold-forging small dimples. Finite element analysis showed that the frequencies of specific mode shapes were differentially affected by the location of residual stress fields due to dimple formation in relation to modal stress fields. The frequencies of overtones were most sensitive to the depth of the dimples located near the maxima of modal stresses. Using this approach a series of musical gongs were designed with up to the first five overtones tuned ..