Me McIntyre

On measuring the elastic and damping constants of orthotropic sheet materials

Abstract Many common sheet materials, ranging from natural materials such as wood to modern composites, possess approximately orthotropic symmetry. Within the approximations of thin-plate bending theory, the linear vibrational properties of such sheets are governed by four elastic constants and four damping constants (at any given frequency). A simple procedure is presented whereby all four elastic constants may be determined, quickly and with reasonable accuracy, from measurements of the resonant frequencies of low-frequency modes of thin rectangular plates with free edges. Also, at least three of the four damping constants may be determined by measuring the damping factors of the same modes—it turns out that the fourth damping constant does not usually have sufficient influence on the low-frequency modes for a reliable value to be found by this approach. The procedure is illustrated with measurements on a range of different sheet materials: wooden plates cut at different angles from the solid timber, plywood, and two very different fibre-reinforced composites. The discussion of these experimental results suggests that this simple procedure could form a valuable part of any programme of quality control, material selection or non-destructive testing involving orthotropic sheet materials.

Friction and the bowed string

Abstract Some aspects of bowed string vibration are discussed with particular emphasis on a regime which is sensitive to details of the friction-velocity characteristics. Apart from its intrinsic interest this study may shed light on the behaviour of other friction-driven oscillators since the rather successful theoretical modelling developed for the bowed string may be applicable to other problems. Conversely, bowed string studies may be able to benefit from the interaction with other work on friction.

Toward understanding violin plate tuning

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.]