A predictive model for the adjustment of violin bows

A finite element model aimed at predicting the in-plane and out-of-plane static mechanical behavior of a tightened bow is developed. It takes into account the prestress due to hair tension and the nonlinear behavior due to large displacements. An non-destructive procedure to determine the input parameters of the model from measurements on a bow is described. Numerical and experimental results are then compared in the case of two bows, showing good agreement between the simulated and measured mechanical behavior. Finally, hair tension and camber are shown to influence the proportion between lateral and vertical compliances of the tightened bow. The model might be used by bow makers for the adjustments of bows during the making process.