Miranda Valiente Pablo, Squicciarini Giacomo, Thompson David J
Institute of Sound and Vibration Research, University of Southampton, Southampton, SO17 1BJ, United Kingdom.
J Acoust Soc Am. 2024 May 1;155(5):3213-3232. doi: 10.1121/10.0025925.
This work explores the influence of the dynamics of the piano soundboard on string vibration and on the force acting between the vibrating string and the bridge. Four different soundboard representations of different complexities are considered: (i) a finite element model that considers the complete dynamic behavior of the soundboard at the connection point with the string within the frequency range of interest, (ii) a reduced modal model containing only five modes, (iii) a Kelvin-Voigt system characterized by an equivalent stiffness and damping, and (iv) a rigid soundboard represented by a simply supported boundary condition. The connection between the string and the soundboard is modelled by coupling a simply supported stiff string model with the different representations of the soundboard through a contact stiffness. As well as directly accounting for the string-soundboard coupling, this approach also includes the duplex scaling segment. The latter can be left to vibrate freely or muted with a continuous distribution of dampers. Although the simplest soundboard representation is not dissimilar from the other more complex models, the dynamics of the soundboard affect the decay time of the note, the force transmitted to it, and the vibration of the radiating surface of the soundboard.
这项工作探讨了钢琴音板动力学对弦振动以及振动弦与琴马之间作用力的影响。考虑了四种不同复杂度的音板表示形式：（i）一个有限元模型，该模型在感兴趣的频率范围内考虑音板在与弦连接点处的完整动态行为；（ii）一个仅包含五个模态的简化模态模型；（iii）一个以等效刚度和阻尼为特征的开尔文-伏伊特系统；（iv）一个由简支边界条件表示的刚性音板。弦与音板之间的连接通过将简支刚性弦模型与音板的不同表示形式通过接触刚度进行耦合来建模。除了直接考虑弦-音板耦合外，这种方法还包括双尺度段。后者可以自由振动或通过连续分布的阻尼器消音。尽管最简单的音板表示形式与其他更复杂的模型并无太大差异，但音板的动力学特性会影响音符的衰减时间、传递到音板的力以及音板辐射表面的振动。
