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

International audienceThe 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