As an example, we would like to introduce physical modeling sound synthesis of cymbals. Since the essence of the cymbal is nonlinearity from a physical point of view, cymbals are also called nonlinear percussion instruments.
Figure 2 shows a physical model of a cymbal. The body of a cymbal is modeled as a shallow spherical shell. In addition, a washer, related to the support conditions of the cymbal, is modeled as a single-degree-of-freedom (SDOF) vibration system and involved in the physical model of the cymbal. Furthermore, a stick/mallet striking the cymbal is considered in the physical model. The mallet head is modeled as an SDOF system having a mass and nonlinear stiffness. The mallet stick is modeled as an Euler-Bernoulli beam and treated as a multi-degree-of-freedom (MDOF) system using the finite element method, and coupled with the cymbal vibration.