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.

Nonlinear vibrations and chaos in gongs and cymbals

“…Experimentations performed on these instruments for many years have shown the typical features of this nonlinear behavior: amplitude-dependent level of harmonics in the spectrum, pitch glide, bifurcations, energy exchange between modes through nonlinear coupling and chaos [1][2][3][4][5][6]. More recently, similar experiments were made on structures of simpler geometry (circular plates, shallow spherical shells) which exhibit comparable effects [7][8][9][10].…”

Transition to chaotic vibrations for harmonically forced perfect and imperfect circular plates

“…The study of the transition from periodic to chaotic vibrations is of primary interest in numerous applied fields such as aeronautic and aerospace or civil engineering, where shell-like structural components are often used [1,2]. Another field where chaotic vibration of shells is searched for, is that of musical acoustics and more precisely the sound of gongs and cymbals where the chaotic nature of the vibration ensures for the peculiar bright and shimmering sound of these instruments [3,4,5,6,7,8]. A convenient and reproducible way to experimentally study the chaotic vibrations of gongs and cymbals consists in harmonically forcing the structure with an increasing amplitude.…”

Analysis of Nonlinearity of the Korean Metal Percussion Instrument, Jing

“…Among them, the representative percussion similar to the Korean percussion instruments, Jing, is a Chinese gong and many researches of that one have been reported [1][2][3][4]. The researches on the Korean Jing and Balinese gamelan gong have been also reported [5][6][7][8].…”