Nonlinear Effects in Drum Membranes

Alberto Torin, Michael Newton

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The linear behaviour of drum membranes has been extensively studied and is now well understood. Particular attention has been devoted to modal analyses of circular drum heads, and good agreement has been found between experiment and theory. Up to now, however, there has been relatively little investigation into the relevance and nature of nonlinear effects in drum membranes.
Stiff strings and stiff plates, however, have seen a good deal of such investigation: pitch glides and the migration of energy towards higher frequencies are typical phenomena that can be found at high striking amplitudes. Such effects result from nonlinearities that arise due to coupling between transverse and longitudinal wave motion in the material.
It has recently been shown that nonlinear effects, similar to those encountered in stiff strings and plates, can be important for drum membranes, both from a physical and a perceptual point of view. While existing tension- modulation techniques provide a useful starting point for modelling the effects of these nonlinearities, a complete nonlinear model is required for a more accurate, and ultimately more realistic, description.
In this study a nonlinear finite difference time domain model of a tom-tom is used, alongside experimental evidence, to highlight and quantify the relevance of nonlinear phenomena in drum membranes. The model includes geometrical membrane nonlinearities, and full air coupling between the two drum membranes. Experimental evidence is obtained from measurements of internal and external sound pressure fields around the drum.
Original languageEnglish
Title of host publicationProceedings of the International Symposium on Musical Acoustics
Place of PublicationLe Mans, France
Pages107-112
Publication statusPublished - Jul 2014

Keywords

  • acoustics
  • musical acoustics
  • nonlinear
  • modelling
  • experiment

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