Geometrical Compensation for Varying Material Properties in Bows by the Use of Numerical Optimization

Wood for violin bows from the pernambuco tree shows large variations in density. For high quality bows, the higher densities are preferred. Since pernambuco is rare and expensive, it is of interest to investigate if it is possible to compensate for variations in density between blanks for bows; particularly in such a way that important qualities of high quality bows are maintained in bows made of wood with a lower density. In this study, numerical optimization is used to replicate some of the static and dynamic properties of a reference bow, using wood with 10% lower density. The structural calculations of the bow are made with a finite element program (ANSYS), which is coupled to an external optimization routine. The automatic optimization process is performed using the Method of Moving Asymptotes. Included are also some remarks on how homogenous scaling of the cross section of a bow of constant length affects some of the static and dynamic properties when used as compensation for density variations.