Numerical simulation of coupled strings with application to physics-based sound synthesis

• Main Author: Orr, Sarah Isobel
• Published: Queen's University Belfast 2013
• Subjects: 781.23
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.602783

The work in this thesis presents and discusses new techniques for modelling string instrument vibrations for the purpose of physics-based sound synthesis. The work focuses on coupled systems, where phenomena such as sympathetic vibrations should naturally occur. Finite difference (FD) methods are chosen for modelling string vibrations for to their flexibility both in terms of local adjustments and possible extensions to nonlinearities. The resonating body is represented using a modal formulation. Modelling the body in such a way has the advantage of scalability which can improve efficiency. This is shown to be possible without affecting the overall timbre of the sound. The models were formulated using idealised shapes such as the beam and plate, but the modal formulation is general for all linear systems. A technique for interfacing the FD model of the string to the modal formulation of the body is presented. In this way the advantages of both methods are exploited, improving the balance between accurate and efficiency. Initially, this coupling is formulated using only transverse motion but is then extended to include longitudinal motion. In simulations of a harp-like instrument where the strings are coupled to the body at an angle, results obtained with numerical experiments show that including longitudinal vibrations impacts the eigenmodes of the system and prove essential for accurately modelling sympathetic vibrations. Comparisons with previous studies validate these results. By applying the proposed method to model resembling a simplified piano, online changes to parameters such as soundboard density further demonstrate the proposed technique.