EXPERIMENTAL CHARACTERIZATION AND COMPUTATIONAL DYNAMIC MODELLING OF A VIOLIN Analysing the effects of creep and string tension

Sammanfattning: During the 17th and early 18th century Antonio Stradivari built around 900 violins, that still today are considered some of the best instruments ever created. The theories of how it was possible for a luthier active 300 years ago to create instruments of this quality are many, including unique wood properties and secret building techniques. The sound of a violin is produced by vibrations from the strings that are transmitted to the top plate and bottom plate through the bridge. The plates and the air in the cavity reverberate within the hollow body, producing the tone characteristic of the violin. Dynamic properties are therefore directly connected to the quality of the instrument. A top and back plate was provided by luthier Robert Zuger. Experimental modal analysis (EMA) was carried out on the plates using the roving excitation technique to determine their modal parameters. Based on the geometries of the plates FE-models of the plates were created. By studying the results of the EMA, material parameters of the plates could be determined in such a way that the modal contents of the FE-plates matched those of the real plates. The natural frequencies for the first 5 modes, extracted from the FE-model, matched those of the real plates within 7 % and the same mode shapes were prevalent in both the FEanalysis and the EMA. Based on violin drawings and input from Robert Zuger a FE-model of a complete violin was created which was tuned by tensioning the strings. The model uses non-linear geometry to handle the effects of string tension. A time-hardening creep model is implemented which can be used to study the aging process of violins. The steady-state response to excitations of the strings were preformed to determine the response of the violin up to 1000 Hz. The mean displacements of the plates were calculated to indicate at which frequencies volume changes of the violin cavity occurred. Each string excitation revealed frequency spans in which the volume change appeared particularly large.