Vibrating plates as musical instruments

Abstract

Vibrating plates are the source of sound in many percussion instruments and also serve as sound radiators in most string instruments. In string instruments the plates vibrate with small amplitude and thus exhibit linear behavior. In some percussion instruments, on the other hand, the initial amplitude may be large enough to introduce nonlinearity. Nonlinear behavior, for example, is largely responsible for the pitch glide noted in certain Chinese gongs [T. D. Rossing and N. H. Fletcher, J. Acoust. Soc. Am. Suppl. 1 70, S23 (1981)]. Plates can exhibit nonlinearities of either the hardening or softening type, depending upon their exact shape and state of stress. The modal frequencies of circular plates vibrating in the linear range can be fitted to a relationship f = c(m + bn)k, where m and n are the numbers of nodal diameters and nodal circles. By proper choice of c it is possible to satisfy Chladni's law (b = 2, k = 2) over quite a wide range of frequency in flat plates. Nonflat plates require different choices of b and k.