Piano hammer: A nonlinear model compared to experiment
Xavier Boutillon · The Journal of the Acoustical Society of America · 1987
This paper presents a nonlinear model for the hammer, its experimental determination, and comparisons between simulated and recorded movements of strings and hammer during their interaction. It is first shown how closely the impact velocity of the hammer is the only input parameter that governs the collision of the hammer with the strings and therefore the quality of the sound. However, this quality is highly dependent on the magnitude of the impact velocity. So, a nonlinear model is required to describe the hammer's behavior. It consists of the association of a mass with a nonlinear, hysteretic spring whose characteristics are experimentally determined under realistic playing conditions. Both nonlinearity and hysteresis are fit by analytical relationships. This model, when associated with a simple flexible string model, allows a numerical simulation of the movements of both hammer and strings. These are compared to the measured vibration of a string and to the measured acceleration of the hammer. In addition, results are presented regarding the efficiency of the hammer impact.