Gonzalez Sebastian, Salvi Davide, Antonacci Fabio, Sarti Augusto
Dipartimento di Elettronica Informazione e Bioingegneria, Politecnico di Milano, Milan, Italy.
J Acoust Soc Am. 2021 Mar;149(3):1400. doi: 10.1121/10.0003599.
We discuss how the modal response of violin plates changes as their shape varies. Starting with an accurate 3D scan of the top plate of a historic violin, we develop a parametric model that controls a smooth shaping of the interior of the plate, while guaranteeing that the boundary is the same as the original violin. This allows us to generate a family of violin tops whose shape can be smoothly controlled through various parameters that are meaningful to a violin maker: from the thickness in different areas of the top to the location, angle, and dimensions of the bass bar. We show that the interplay between the different parameters affects the eigenmodes of the plate frequencies in a nonlinear fashion. We also show that, depending on the parameters, the ratio between the fifth and the second eigenfrequencies can be set to match that used by celebrated violin makers of the Cremonese school. As the parameterisation that we define can be readily understood by violin makers, we believe that our findings can have a relevant impact on the violin making community, as they show how to steer geometric modifications of the violin to balance the eigenfrequencies of the free plates.
我们讨论了小提琴面板的模态响应如何随着其形状的变化而改变。从一把历史悠久的小提琴面板的精确三维扫描开始，我们开发了一个参数模型，该模型控制面板内部的平滑塑形，同时确保边界与原始小提琴相同。这使我们能够生成一系列小提琴面板，其形状可以通过对小提琴制作师有意义的各种参数进行平滑控制：从面板不同区域的厚度到低音梁的位置、角度和尺寸。我们表明，不同参数之间的相互作用以非线性方式影响面板频率的本征模式。我们还表明，根据参数的不同，第五和第二本征频率之间的比率可以设置为与克雷莫纳学派著名小提琴制作师所使用的比率相匹配。由于我们定义的参数化很容易被小提琴制作师理解，我们相信我们的发现可能会对小提琴制作界产生相关影响，因为它们展示了如何引导小提琴的几何修改以平衡自由面板的本征频率。
