Consultation des notices

A model of the vibrational coupling between the strings, the bridge and the soundboard of the piano in its treble register is presented. Each one of these vibrating structures is separately described by its mechanical input admittance matrix in which the nine terms represent impulse responses or frequency responses to a vectorial input force. The total admittance matrix is analytical and is calculated by assembling the latter in accordance with classical mechanical continuity equations. This formalism allows to study the role of each part of the system by simulating the interaction between a chosen number of structures. Simulations show that the two perpendicular polarisations of bending motion of a single string influence each other due to the elastic response of the bridge. Similar to this is the coupling between unison strings. These interactions give rise to beats and double decay phenomena, which are of particular interest to professional piano makers and tuners. The influence of sound radiation by the soundboard and of duplex strings on the temporal behaviour of the piano and on the spectral content of vibrations is discussed as well. Simulations will be presented and discussed comparing them to experimental work carried on a simplified piano.