The vibratory behaviour of the piano soundboard in the mid-frequency domain is studied in this PhD thesis. The first chapter is devoted to the board itself: its role, structure and materials. An exhaustive bibliographical study is presented and the main published results are given and synthesised. The second chapter introduces a new modal analysis technique based on a high-resolution analysis algorithm. The technique resolves cases where the Fourier transform performs poorly due to its natural DeltaT.DeltaF limitation. This new method is assessed by comparing experimental and theoretical partial modal analyses of aluminium thin plates up to a modal overlap of 70%. The modal identification of an upright piano soundboard is partly achieved with this method in the mid-frequency domain [300-2500 Hz]. The estimation of the mean loss-factors of the spruce board in this frequency domain is a new result. The frequency dependency of the observed modal density of the ribbed-board below 1.1 kHz contributes to define an equivalent homogeneous plate. Above 1.1 kHz, the soundboard behaves like a set of waveguides. The modal shapes obtained through a finite-element model confirm the localisation of the waves between the ribs. On such a structure, the acoustical coincidence phenomenon is deeply modified in comparison to the one occurring in thin plates. The purpose of the last chapter is to propose a synthetic description of a piano soundboard based on a small number of global descriptors: overall dimensions, aspect ratio, mass, modal density, mean loss factor, average distance between two consecutive ribs. The validity of an equivalent homogeneous plate model is studied and the replacement of the structure by a plate in composite material is considered. The synthetic description can be used to predict the changes of the driving-point mobility (at bridge) and of the sound radiation in the treble range resulting from structural modifications (changes in material, geometry, average ribs spacing, etc.).
The piano soundboard - Modal studies in the low- and the mid-frequency range