Nonlinearity, chaos, and the sound of shallow gongs

Abstract

Experimental studies on several orchestral gongs of the tamtam and cymbal families suggest that two separate nonlinear mechanisms contribute to the evolution of the sound. The first mechanism is an upward cascade of energy from the low‐frequency modes initially excited into high‐frequency modes, caused by coupling between tension and shear stresses at regions of sharp change in shape of the gong. The second is a transition from simple periodic nonlinear modal motion to multiple fractional subharmonics, or even chaotic motion, which fills out the radiated spectrum at frequencies between those of the normal linear modes. Each of these mechanisms has considerable hysteresis, so that the spectrum of the radiated sound evolves over a period of several seconds. Measurements using high‐level sinusoidal excitation have elucidated some of the features of this behavior.