Modeling the interaction between piano strings and the soundboard
Pablo Miranda Valiente, Giacomo Squicciarini, David Thompson · Proceedings of meetings on acoustics · 2022
In a piano, the different polarizations of string vibration and the coupling with the soundboard play an important role in tone generation. This study shows how these features can be included in a modal model of the string-soundboard system and analyzes the role played by the mobility matrix of the soundboard at the connection point. The coupling between the string and soundboard is implemented using different approaches. First, a linear frequency-domain model is developed and used to demonstrate the importance of the direct and cross terms of the soundboard mobility matrix. A comparison is presented between a full Finite Element solution and a simplified soundboard representation. Subsequently, to represent the process of sound generation in a piano, a time domain solution is adopted. An analysis of the frequency-domain results shows that the coupling between the two transverse directions is significant, while the longitudinal vibration plays a smaller role. In addition, it is found that the difference between a detailed Finite Element model and a simpler approach for the soundboard is small for string vibration. Time-domain results are presented to analyze the effect of double polarization. This leads to an assessment of the double decay and multidirectional forcing of the bridge.