Vibration analysis of piano strings involving dynamics of hammer shanks

Abstract

In this study, we develop a physical model of a grand piano string involving a high-fidelity expression of hammer shank dynamics. A hammer shank is modeled as a general beam, and its governing equation is analyzed using the finite element method (FEM). In addition, the rotational motion of the hammer shank is explicitly expressed and incorporated into the formulation of the FEM. The developed method also involves a more general physical model of piano strings, which is numerically analyzed using the finite difference method (FDM). The proposed method is validated by comparing numerical results with previously reported measurement results.