Nonlinear physical modeling sound synthesis of cymbals involving dynamics of washers and sticks/mallets

Abstract

This paper is concerned with the extension of the existing nonlinear physical modeling sound synthesis of cymbals to that involving the dynamics of washers supporting the center of cymbals and sticks/mallets striking the cymbals. The body of a cymbal is physically modeled as a shallow spherical shell and its governing equation is discretized in space using the finite difference method, as was implemented in existing research. In addition, a washer, related to the support conditions of the cymbal, is modeled as a single-degree-of-freedom vibration system and involved in the physical model of the cymbal. Furthermore, a stick/mallet striking the cymbal is also involved by modeling it as a multi-degree-of-freedom system using the finite element method and coupled with the cymbal vibration. The time-domain differential of the total system is discretized using implicit finite difference schemes. Trial numerical calculations demonstrate that the developed method is effective in the sound synthesis of the cymbal, grasping the change of timbre due to the dynamics of washers and sticks/mallets.