The impact of alkaline treatments on elasticity in spruce tonewood

Abstract

It is commonly believed that violins sound differently when finished. However, if the role of varnishes on the vibrational properties of these musical instruments is well-established, how the first components of the complete wood finish impact on the final result is still unclear. According to tradition, the priming process consists of two distinct stages, called pre-treatment and sizing. The literature reports some recipes used by old Cremonese luthiers as primers, mainly based on alkaline aqueous solutions and protein-based glues. In this manuscript, we analyze the impact of these treatments on the mechanical properties of the material. The combination of two pre-treatments and three sizes is considered on nine different plates. We compare the vibrational properties before and after the application and assess the effects of the different primers, also supported by finite element modeling. The main outcome is that the combination of particular treatments on the violin surface before varnishing leads to changes not only to the wood appearance, but also to its vibrational properties. Indeed pre-treatments, often considered negligible in terms of vibrational changes, enhance the penetration of the size into the wood structure and strengthen the impact of the latter on the final rigidity of the material along the longitudinal and radial directions.

Figure 1

(a) Diagram of the plate geometry, with the location of the excitation (highlighted in orange) and measurement ( highlighted in light blue) points chosen for hammer impact testing. (b) Table listing the nine Spruce plates and details on the different primers applied.

Figure 2

Comparison between FRF measured (in cyan) and FEM simulation (in orange) obtained with the estimated elastic constants. In the example, plate 4 is considered. The resulting magnitudes are normalized between 0 and 1. Measurements from white specimens were fitted as in and using Rayleigh damping with constants $\alpha =10$ [${\text{s}}^{-1}$] and $\beta =2\times {10}^{-6}$ [s], according to. The eigenfrequencies obtained numerically and corresponding to resonances in the measure are highlighted with dashed red lines. In the measurement points chosen, modes with a nodal line along the longitudinal axis of symmetry are attenuated, e.g. (1,1) (colored in gray), making the peaks of interest easier to identify. The mode shape associated to each resonance is depicted above the plot, denoted with a notation based on nodal lines and widely used in the literature.

Figure 3

Relative variation in the longitudinal and radial specific stiffness observed at the end of each treatment stage (green: pre-treatment, orange: sizing). Values are expressed in percentage and represented with squares. Error bars represent the estimation error. Left: Estimated variation for the longitudinal specific stiffness $\delta ({\widehat{E}}_L/\widehat{\rho })$, with a maximum error of 2.7%; Right: Estimated variation for the radial specific stiffness $\delta ({\widehat{E}}_R/\widehat{\rho })$, with a maximum error of 3.0%. Estimations are based on Caldersmith’s equations, assuming the contribution of Poisson’s ratios as negligible.

Figure 4

(a) Diagram of the transversal profile assumed in the FE model for the characterization of the treated side of the specimen. (b) Distribution of penetration depths $h_l$ making the FE model best approximate the modal frequencies of plates 1-3, only sized. (c) Distribution of penetration depths $h_l$ making the FE model best approximate the modal frequencies of plates 4-6, pre-treated with KOH. (d) Distribution of penetration depths $h_l$ making the FE model best approximate the modal frequencies in plates 7-9, pre-treated with ${\text{NH}}_3$. Histograms are evaluated when plates are only pre-treated ($t=p$, dashed lines) and after the application of the complete primers ($t=s$, solid lines). Colored regions highlight the ranges of preferential values characterizing each combination of treatments.

Figure 5

Left: Semi-quantitative line profiling of potassium (K) analyzed with SEM-EDX on plates subject to potassium-based treatments (i.e. involving KOH and C). The lines represent the potassium concentration evaluated at different depths while colored regions highlight the feasible limits of interaction between the wood and the different treatments. The limits were estimated by fitting a bilinear model to each profile decay; Right: Comparison between the penetration depths estimated from SEM-EDX profiles (yellow bars) and the mean values of the preferential depth ranges found through FE analysis (violet bars). The analysis is limited to plates subject to potassium-based treatments.

Figure 6

Left: Distribution of changes in the equivalent density of the FE model $\delta \rho$. The equivalent density is obtained as the weighted sum of the estimated layer density ${\rho }_l$ and the density measured originally. The weights used are the penetration depth $h_l$ and $h-h_l$, respectively. Histograms are computed after both the treatment stages (pre-treatment: green, sizing: orange) collecting the values in percentage such that the FE model best approximate the modal frequencies in each plate. Dashed lines correspond to the histogram fits by means of Gaussian probability density functions; Right: Gaussian fit for $\delta \rho$ after the sizing stage, computed for plates grouped by pre-treatment used. Pre-treatments induce a density increase due to the sizing which is greater than the variation encountered if plates are only sized.