On operating deflection shapes of the violin body including in-plane motions

Earlier investigations have assumed only "out-of-plane" vibrations of the plates of the violin. The violin body can, however, be described as a thin-walled, double-arched shell structure and as such it may very well elongate in one direction as it contracts in another. Therefore, at least two orthogonal vibration components have to be included to describe the vibrations. The operating deflection shapes (ODSs) of a good, professionally made and carefully selected violin were therefore measured in several directions by TV holography to determine both "in-plane" and out-of-plane vibration components of the ODSs. The observations were limited to the frequency range 400-600 Hz, as this interval includes two most-prominent resonance peaks of bridge mobility and sound radiation as well as a third poorly radiating resonance. These three peaks clearly showed orthogonal vibration components in the ODSs. The vibration behavior of the violin body, sectioned in the bridge plane, was interpreted as the vibrations of an "elliptical tube" with nodal diameters. The number of nodal diameters increases from two to three in the selected frequency range. The TV holography measurements were supported by electrodynamical point measurements of bridge mobility, of air volume resonances, and by reciprocity, of radiation properties. Furthermore, a fourth mode, the air mode, A1, is involved indirectly in the sound radiation via influence on the body vibrations.