A numerical model for the 3-D non-linear vibrations of an N-string

We present a non-linear numerical model describing the 3-D vibrations of a planar network of N sections of string which are connected together at one common mobile extremity. We call such a network N-string. For small-amplitude vibrations perpendicular to the N-string equilibrium plane, the numerical results coincide with the already known analytical solutions of the linear model. This non-linear model makes it possible to describe small- or large-amplitude 3-D vibrations of any kind of N-string subjected to an initial plucking. The equations of motion are also presented in a dimensionless form and a vast dimensionless physical parameter space is identified. The numerical model can be extended to more complex networks of strings.