Physical modeling and time-domain simulation of a piano

The elaborate method to simulate the sound produced by a piano is presented, using the physical model that considers almost all parts of the piano with wood complex elastic orthotropy and manufacturing stress, but excluding action parts. The purpose of this work is to improve the efficiency of piano development by clarifying the causal relationship between the design and the produced sound. The completed piano is modeled as a 3D coupled system consisting of “nonlinear systems including hammers and strings” and “a linear coupled body-air system.” The hammer felt property are represented by the double layer nonlinear generalized Maxwell model. For the strings with geometrical nonlinearity and their support end anisotropy, the Galerkin method with the component mode synthesis (CMS) method is applied. And also, for the large-scale linear coupled body-air system, the complex CMS method via nonlinear eigenvalue analysis is used. The simulated sounds, including the ringing and body sounds, are so realistic that they help piano designers predict the actual sounds before making heavy prototypes. The method presented here can be applied to other musical instruments that consist of strings and a body, such as guitars and violins.