The aim of this article is to correlate the experimental modal analysis (EMA) with finite element analysis (FEA) to study the effect of wood species on vibration modes of violin plates made of spruce and maple. For EMA, five violin plates each made of spruce and maple were tested (curly maple, quilted maple, common maple with regular and irregular rings). The plates were clamped on edges and subjected to forced vibration. Experimental Chladni patterns of these plates were determined for 36 emitted frequencies, range between 65 and 2637 Hz. Patterns obtained with modal analysis are characterised by the nodal lines. The patterns of vibration modes are affected by wood species and structure. Spruce plate shows nodal lines aligned to the longitudinal (L) anisotropic direction of wood, corresponding to the direction of the fibres. Maple plates show nodal lines aligned to radial (R) anisotropic direction of wood and to the direction of medullary rays in the LR plane. Curly maple plate vibration produced the best resolution of vibration modes pattern, because of the presence of very abundant medullary rays, well oriented in the R direction. Quilted maple plate has asymmetric modes of vibration. At the highest frequency of 2093 Hz, no vibrating zones were observed during the experiment. Maple plates of normal structure with regular and irregular annual rings have shown similar patterns, but differ from curly maple plate. The characteristics of annual rings were measured. The vibrating surfaces (S_v) of the plates obtained experimentally were measured by transferring the nodal lines into AutoCAD 2013 software, where the surfaces were computed and expressed in mm² or in % of the total surface area of the plate; the total effective vibrating surface for all frequencies for each plate and wood species; the relative vibrating surface at maximum amplitude. The experimental results were compared to modal analysis performed with FEA, by using ABAQUS program. The similar geometry of the real plates was generated in ABAQUS and the violin plates were meshed with quadratic shell elements. The plates were modelled as orthotropic materials. At maximum vibration amplitude and frequency of 110 Hz, the spruce plate has a relative vibrating surface of 62%, a mean annual ring width of 0.77 mm and ring heterogeneity of only 64%. At maximum amplitude of vibration and frequency of 174 Hz, the plates made of curly maple LR and LT (longitudinal–tangential), have different behaviour. The vibrating surface is greater for the plate made of curly maple LR with dense figures (84%) and annual ring heterogeneity of 86%, than for plates made of curly maple LT with large figures (77%) and annual ring heterogeneity of 238%.

中文翻译：

---

木材种类对小提琴板振动模式的影响

本文旨在将实验模态分析（EMA）与有限元分析（FEA）相关联，以研究木材种类对云杉和枫木制成的小提琴板振动模式的影响。对于EMA，测试了五个分别由云杉和枫木制成的小提琴板（卷曲枫木，缝枫木，带规则和不规则环的普通枫木）。将板夹在边缘上并使其受到强制振动。确定了这些板的实验Chladni模式的发射频率为36，范围在65和2637 Hz之间。通过模态分析获得的模式以结线为特征。振动模式的模式受木材种类和结构的影响。云杉板显示的节线与木材的纵向（L）各向异性方向对齐，该方向对应于纤维的方向。枫板显示出与木材的径向（R）各向异性方向和LR平面中的髓射线方向对齐的结线。卷曲的枫板振动产生了最佳的振动模式图分辨率，这是因为存在非常丰富的沿R方向定向的髓线射线。map缝的枫板具有不对称的振动模式。在2093 Hz的最高频率下，实验过程中未观察到振动区。具有规则和不规则年轮的正常结构的枫板显示出相似的模式，但不同于卷曲的枫板。测量了年轮的特征。振动面（S 卷曲的枫板振动产生了最佳的振动模式图分辨率，这是因为存在非常丰富的沿R方向定向的髓线射线。map缝的枫板具有不对称的振动模式。在2093 Hz的最高频率下，实验过程中未观察到振动区。具有规则和不规则年轮的正常结构的枫板显示出相似的模式，但不同于卷曲的枫板。测量了年轮的特征。振动面（S 卷曲的枫板振动产生了最佳的振动模式图分辨率，这是因为存在非常丰富的沿R方向定向的髓线射线。map缝的枫板具有不对称的振动模式。在2093 Hz的最高频率下，实验过程中未观察到振动区。具有规则和不规则年轮的正常结构的枫板显示出相似的模式，但不同于卷曲的枫板。测量了年轮的特征。振动面（S 具有规则和不规则年轮的正常结构的枫板显示出相似的模式，但不同于卷曲的枫板。测量了年轮的特征。振动面（S 具有规则和不规则年轮的正常结构的枫板显示出相似的模式，但不同于卷曲的枫板。测量了年轮的特征。振动面（S_v）通过将节点线转移到AutoCAD 2013软件中来测量实验获得的板，在其中计算表面并以mm ²表示或以板总表面积的百分比表示；每种板材和木材种类在所有频率下的总有效振动表面；最大振幅的相对振动表面。通过使用ABAQUS程序，将实验结果与用FEA进行的模态分析进行了比较。在ABAQUS中生成了与实际板相似的几何形状，并将小提琴板与二次壳单元啮合。将板建模为正交各向异性材料。在最大振动幅度和频率为110 Hz时，云杉板的相对振动表面为62％，年平均环宽度为0.77 mm，环的异质性仅为64％。在最大振动振幅和174 Hz的频率下，由卷曲枫木LR和LT（纵向切线）制成的板具有不同的行为。