PIANO HAMMER-STRING INTERACTION: THE INFLUENCE OF THE ELASTIC PARAMETERS OF BASS HAMMERS ON THE CONTACT TIME DURATION
Anatoli Stulov, Dmitri Kartofelev · 2009
The influence of the elastic parameters of the bass hammers on the contact time duration is analyzed by physics-based mathematical modeling of the hammer string interaction. Two models that accomplish this with numerical calculation are described, and sample results are presented. The first model is based on the nonlinear hysteretic model of piano hammer that is in a good agreement with experimental data, and gives the possibility to calculate the motion of strings and hammers, and to simulate the piano hammer-string interaction. The second model takes into account that the mass of bass hammer is much less than the mass of the string, and it makes possible to consider the hammer-string interaction as a hammer strike against a rigid surface. According to these models (and in reality), the contact time duration of a hammer strike decreases with increasing of the hammer velocity. It means that the speed of a compression wave, traveling from the contact point to the hammer kernel and back, increases with the growth of its amplitude. Both models give similar predictions for the duration of the hammer strike.