Modal-Type Synthesis Techniques for Nonlinear Strings with an Energy Conservation Property
There has recently been increased interest in the modelling of string vibration under large amplitude conditions, for sound synthesis purposes. A simple nonlinear model is given by the KirchhoffCarrier equation, which can be thought of as a generalization of the wave equation to the case for which the string tension is “modulated” by variations in the length of the string under deformation. Finite difference schemes are one means of approach for the simulation of nonlinear PDE systems; in this case, however, as the nonlinearity is spatially invariant, the solution may be broken down into sinusoidal components, much as in the linear case. More importantly, if time discretization is carried out in a particular way, it is possible to obtain a conserved energy in the numerical scheme, leading to a useful numerical stability guarantee, which can be difficult to obtain for strongly nonlinear systems. Numerical results are presented.