Experimental study of nonlinear phenomena in an upright piano.

Abstract

Measurements are conducted on an upright piano in order to investigate the nonlinear dynamics of the instrument from the blow of the hammer to the radiated sound in the nearfield. The experimental setup consists in synchronous recording of eight channels: hammer force, string displacement at various points, velocity and force at bridges, soundboard acceleration, and sound pressure. From these measurements, the transmission of vibrations through the instrument is followed in both the time and frequency domains. Excitation of strings at different amplitudes shows the influence of the geometrical nonlinear phenomena in the radiated sound. In the time domain, the most visible consequence of nonlinearity is the presence of a precursor in the force and acceleration waveforms at the bridge. To clearly discriminate between dispersion precursor, due to stiffness, and nonlinear precursor, experiments are conducted on two strings corresponding to limiting cases: the C2 string, where stiffness is dominant, and the E3 string where the geometrical nonlinear effects are preponderant. Fine spectral analysis shows that the transmission of energy from strings to soundboard at the bridge is crucial in enhancing the level of phantom partials in the emitted sound due to quadratic and cubic nonlinearities in the string force.