Effect of the wood anisotropy on eigenmodes and eigenvalues using finite element analysis – case of violin plates

The paper presents numerical studies performed with FEA related to the effect of wood anisotropy on vibration modes of violin plates made of spruce (Picea abies) and maple (Acer pseudoplatanus). The two-wood species are the traditional species for the top and back of the violins. In this study, three hypotheses – the material is isotropic; the material is transverse isotropic; the material is orthotropic, was used for modal analysis of violin plates. The plates were considered flat and having uniform thickness of 3 mm. Patterns obtained with modal analysis of violin vibration plates are illustrated for low frequencies modes and were compared to experimental results. The effect of anisotropy was illustrated by the variation of modal frequency of plates with the frequency of resonance modes. The difference between modal frequencies for the modes 6, 9, 10 and 12, calculated for the plate made of spruce and for the plate made of maple having orthotropic symmetry is respectively between 1.38% and 7%. For isotropic symmetry and for the same modes, this difference for the plate made of spruce and maple varies respectively between 57% and 18.92 %. The effect of anisotropy on the modal frequency of plate made of maple is more important than that on plate made of spruce.