EXPERIMENTAL AND THEORETICAL STUDIES OF PIANO HAMMER

Based upon the large number of experimental data obtained using a special piano hammer testing device, it has been shown, that all the present-day piano hammers have as a quality the hysteretic type of the force-compression characteristics. This not a chance because such a hysteretic character has been developed step-bystep following the history of evolution of piano hammers since the instrument was created. The dynamical behaviour of the modern piano hammer can be described by different mathematical hysteretic models. In addition to the four-parameter nonlinear hysteretic model of piano hammer, another new three-parameter hysteretic model was developed. It is very similar to the nonlinear Voigt model and permits a description of the dynamical hammer felt compression that is consistent with experiments. The both models are based on an assumption that the hammer felt made of wool is a microstructured material possessing history-dependent properties. The equivalence of these models is proved for all the realistic values of hammer velocity. The continuous dependencies of the hammer parameters on the key number are obtained, which is the first known case of such an analysis. The application of hysteretic models to numerical simulation of the grand piano hammer-string interaction is demonstrated. The flexible string vibration spectra excited by different piano hammers are analyzed. All that together, leads to a new method for piano stringing-scale design.