A dynamical multibody approach for guitar modelling incorporating string geometric nonlinear effects

Most musical instruments consist on dynamical subsystems connected at a number of constraining locations. For physical sound synthesis, one important difficulty deals with the manner to enforce these coupling constraints. While standard techniques include the use of Lagrange multipliers or penalty methods, we explore in this paper a different approach, the Udwadia-Kalaba (U-K)
formulation, which is rooted on analytical dynamics but avoids the use of Lagrange multipliers. Following our recent work, we generalize this modelling framework to a multibody flexible system such that each component is defined by its unconstrained modal basis, and then compute the string/body coupled dynamics of a guitar. Moreover, the generality of this computational
technique is demonstrated by incorporating the string geometrical nonlinear effects in the model, using the Kirchoff-Carrier (K-C) simplified approach. The guitar model obtained is computationally effective and the illustrative results presented highlight the significance of the nonlinear string effects for plucked string instruments, which lead to clearly audible modal coupling terms and frequency gliding effects.