Scalar Auxiliary Variable Techniques for Nonlinear Transverse String Vibration

Abstract

The simulation of string vibration is of fundamental importance in musical acoustics. If the vibration amplitude is large then nonlinear phenomena, resulting from large deformations, cannot be neglected, and lead to perceptually salient features. Energy-conserving simulation algorithms found in the literature rely on tailored discretisation choices, making them model–specific. Recently, energy quadratisation–based techniques have been developed, under the assumption that the potential energy is single-signed. These methods allow for the solution of a variety of different nonlinear systems with the same time-stepping procedure, requiring only the evaluation of a specific nonlinear potential. Moreover, they possess an exact numerical energy conservation property, and permit efficient operation. Such methods were previously employed for solving nonlinear string models. In this paper, nonlinear models of transverse string vibration are first semi-discretised in space by means of both finite differences and modal methods. The resulting equations are solved through the use of the Scalar Auxiliary Variable (SAV) technique. Results are then compared against those obtained with model – specific numerical integrators in terms of Efficiency and accuracy.