In this study, the influence of “bear claw” or indented growth ring anatomical patterns on the vibro-mechanical behavior of spruce wood have been investigated, particularly in the context of utilizing these singularities/specific features for the construction of violins. By employing vibrometry and modal analysis followed by finite element model updating, the vibro-mechanical properties (specific stiffness in longitudinal (L) and radial (R) directions and shear LR plane, and associated damping) of the indented growth rings spruce were identified and implemented in a numerical model of a violin. Results have revealed a significant increase in specific moduli in R direction and LR plane and decrease in L direction of spruce wood in the presence of indented growth rings, therefore accompanied by a reduction in anisotropic elastic properties, in comparison to spruce without these patterns. These properties led to changes in violin dynamics, globally increasing resonance frequencies and changing the shape of the vibration modes. The simulated frequency response function of the violin at the bridge suggested a global shift of the admittance of the bridge toward higher frequencies. These results suggest a potential impact of indented growth rings of spruce on the acoustic properties of instruments.

中文翻译：

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锯齿状年轮对云杉木材力学性能及后续小提琴动力学的影响

在这项研究中，研究了“熊爪”或锯齿状生长环解剖模式对云杉木振动机械行为的影响，特别是在利用这些奇点/特定特征来制造小提琴的背景下。通过采用振动测量和模态分析，然后更新有限元模型，确定了锯齿状年轮云杉的振动机械特性（纵向 (L) 和径向 (R) 方向和剪切 LR 平面的比刚度，以及相关阻尼），在小提琴的数值模型中实现。结果表明，与没有这些图案的云杉相比，在存在锯齿状年轮的情况下，云杉木材的 R 方向和 LR 平面的比模量显着增加，L 方向的比模量显着增加，因此伴随着各向异性弹性特性的降低。这些特性导致了小提琴动力学的变化，整体增加了共振频率并改变了振动模式的形状。琴桥处小提琴的模拟频率响应函数表明琴桥的导纳整体向更高频率移动。这些结果表明云杉的锯齿状年轮对乐器的声学特性具有潜在影响。