Modal analysis of a grand piano soundboard at successive manufacturing stages

This paper deals with the development and validation of a finite element numerical model of a grand piano soundboard. The most important details of the manufacturing process are reproduced in this model. In particular, by modelling the gluing of the ribs and the bridges to the board, the curved geometry (the crown) and the residual stresses induced in the soundboard are taken into account. Experimental modal analysis results are presented at three stages of the manufacturing process of the same soundboard: (i) freely suspended soundboard before gluing the bridges, (ii) freely suspended soundboard including the two bridges, and (iii) soundboard attached to the piano frame. The experimental data at the first of these three stages are used to update the material properties of the finite element model, so as to minimise the difference between calculated and experimental vibration modes, in terms of both natural frequencies and mode shapes. The simulation of the other manufacturing stages is then performed without any additional tuning. Vibration modes obtained from experiments up to 400–450 Hz are compared with those obtained through the numerical model. Point mobilities measured on the bridge at the different manufacturing stages are also shown and discussed. Above 200 Hz, the mobilities measured on the bridge of the freely suspended soundboard and on the bridge of the soundboard fixed to the frame are very similar, thus showing that in this frequency range the effect of the soundboard local dynamic stiffness is predominant over boundary conditions. Finally, point mobility at the bridge is also calculated through the finite element model and compared to the experiments, with good agreement up to 4 kHz.