Buckling Instability of a Violin Bow
Résumé
This paper addresses the phenomenon of lateral buckling that could occur on an improperly adjusted violin bow during playing. A finite-element model taking into account geometric nonlinearity is used to simulate the static response of a tightened bow to the applied bow force. It is shown that the addition of a small lateral perturbation load enables out-of-plane buckling of the stick once the bow force reaches a certain value. The link between this critical bow force and the critical tension of the bow is clarified. The way the perturbation load smoothes the transition between in-plane and out-of-plane deformation of the stick is illustrated. The influence of camber (curvature of the stick) on buckling is examined. A possible way to increase the lateral stability of a bow without altering its vertical stiffness is proposed.