Physical modeling leads to efficient and scalable simulation algorithms in the discrete time domain, which are used in real-time music applications. Many percussive instruments are physically described by Kirchhoff's thin plate equation. Considering a complete system, e.g. the single plates of a xylophone, the oscillation behavior can be described by a partial differential equation and the connection to the suspension by a set of boundary conditions. Problems described like that are known as initial-boundary value problems and can be modeled by an expansion into a suitable set of eigenfunctions. The solution is formulated in terms of a multi-dimensional state-space description in a spatio-temporal transform domain, which proves to be helpful for the incorporation of complex boundary conditions. The results of the model are validated by simulations of the plate deflection.
