Toward understanding violin plate tuning

Abstract

As Hutchins has shown, violin makers observe a surprising sensitivity, to small plate-thickness perturbations, of the internal damping of vibration modes of violin plates. Progress towards a systematic theory of this phenomenon is reported. The method used provides a simple framework for describing the effect on internal damping of mode shape, boundary conditions, and geometry for a wide class of materials. One important fact to emerge is that more material parameters may enter than have traditionally been measured, and indeed the usual measurement technique employing thin strips is seen to be incapable of measuring them. A more suitable technique using flat plates is described and illustrated with some computations and preliminary experimental results. These confirm the prediction that “plate-tuning effects” similar to those found in wooden violin plates can also occur in isotropic plates, for frequencies well below the level where shear motion needs to be taken into account. [We thank the Science Research Council for financial support and the Cambridge University Engineering Department for providing experimental facilities.]