SOUND SYNTHESIS OF GONGS OBTAINED FROM NONLINEAR THIN PLATES VIBRATIONS: COMPARISON BETWEEN A MODAL APPROACH AND A FINITE DIFFERENCE SCHEME

Michele Ducceschi, Cyril Touze, Stefan Bilbao

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

Abstract

The sound of a gong is simulated through the vibrations
of thin elastic plates. The dynamical equations are necessarily nonlinear, crashing and shimmering being typical
nonlinear effects. In this work two methods are used to
simulate the nonlinear plates: a finite difference scheme
and a modal approach. The striking force is approximated
to the first order by a raised cosine of varying amplitude
and contact duration acting on one point of the surface. It
will be seen that for linear and moderately nonlinear vibrations the modal approach is particularly appealing as it allows the implementation of a rich damping mechanism by
introducing a damping coefficient for each mode. In this
way, the frequency-dependent decay rates can be tuned to
get a very realistic sound. However, in many cases cymbal
vibrations are found in strongly nonlinear regimes, where
an energy cascade through lengthscales brings energy up
to high-frequency modes. Hence, the number of modes
retained in the truncation becomes a crucial parameter of
the simulation. In this sense the finite difference scheme is
usually better suited for reproducing crash and gong-like
sounds, because this scheme retains all the modes up to
(almost) Nyquist. However, the modal equations will be
shown to have useful symmetry properties that can be used
to speed up the off-line calculation process, leading to large
memory and time savings and thus giving the possibility to
simulate higher frequency ranges using modes.
Original languageEnglish
Title of host publicationProceedings of the Stockholm Musical Acoustics Conference/Sound and Music Computing Conference
Place of PublicationStockholm, Sweden
Number of pages8
Publication statusPublished - Aug 2013

Fingerprint

Dive into the research topics of 'SOUND SYNTHESIS OF GONGS OBTAINED FROM NONLINEAR THIN PLATES VIBRATIONS: COMPARISON BETWEEN A MODAL APPROACH AND A FINITE DIFFERENCE SCHEME'. Together they form a unique fingerprint.

Cite this