A Modal Method for the Simulation of Nonlinear Dynamical Systems with Application to Bowed Musical Instruments

Bowed instruments are among the most exciting sound sources in the musical world, mostly because of the expressivity they allow to a musician or the variety of sounds they can generate. From the physical point of view, the complex nature of the nonlinear sound generating mechanism – the friction between two surfaces – is no less stimulating. In this thesis, a physical modelling computational method based on a modal approach is developed to perform simulations of nonlinear dynamical systems with particular application to friction-excited musical instruments. This computational method is applied here to three types of systems: bowed bars, such as the vibraphone or marimba, bowed shells as the Tibetan bowl or the glass harmonica and bowed strings as the violin or cello. The successful implementation of the method in these instruments is shown by comparison with measured results and with other simulation methods. This approach is extended from systems with simple modal basis to more complex structures consisting of different sub-structures, which can also be described by their own modal set. The extensive nonlinear numerical simulations described in this thesis, enabled some important contributions concerning the dynamics of these instruments: for bowed bars the simulated vibratory regimes emerging from different playing conditions is mapped; for bowed Tibetan bowls, the essential introduction of the radial and tangential mode pairs characteristic of axi-symmetrical structures is performed, enabling an important clarification on the beating phenomena arising from the rotating behaviour of oscillating modes; for the bowed string an effective simulation of a realistic wolf-note on a cello was obtained, using complex identified body modal data, showing the beating dependence of the wolf-note with bowing velocity and applied bow force, with good agreement with measured results. Furthermore, a linearized approach to the nonlinear problem is implemented and the results compared with the nonlinear numerical simulations.

Year 2013
Type Thesis
Institution Institute of Sound and Vibration Research (ISVR), University of Southampton, UK
Degree PhD
Supervisor(s) José Vieira Antunes, Matthew Wrigth, Joe Hammond
Language English
Field Musical Acoustics