Modelling and Optimization of Stringed Musical Instruments

Wolfgang Ring^*

We discuss several aspects of modelling and optimization of stringed (and bowed) instruments. The excitation of the string by the bow is discussed and the fact that the bowed string vibrates with the fundamental frequency of the plucked string is investigated on the basis of a model for the friction between bow and string. Control problems arise naturally when asking for bow speed and bow pressure to produce a stable periodic motion with a short transient period. Further problems in connection with modelling and estimation of parameters and (possible) optimal parameter choices for typical quality criteria of stringed instruments are presented.

Mathematics Subject Classification: 74G75 74P10

Keywords: vibrating systems; sensitivity analysis; inverse eigenvalue problem

Minisymposion: Inverse Problems in Elasticity