Effect of wood species on vibration modes of violins plates

摘要

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 mm(2) 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%.