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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 frequencydependent 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 highfrequency 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 gonglike
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 offline calculation process, leading to large
memory and time savings and thus giving the possibility to
simulate higher frequency ranges using modes.
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 frequencydependent 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 highfrequency 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 gonglike
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 offline calculation process, leading to large
memory and time savings and thus giving the possibility to
simulate higher frequency ranges using modes.
Original language  English 

Title of host publication  Proceedings of the Stockholm Musical Acoustics Conference/Sound and Music Computing Conference 
Place of Publication  Stockholm, Sweden 
Number of pages  8 
Publication status  Published  Aug 2013 
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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.Projects
 1 Finished

NESS  Listening to the future: Nextgeneration Sound Synthesis through Simulation
1/01/12 → 31/12/16
Project: Research