Nonlinear modelling of the middle ear as an elastic multibody system — Applying model order reduction to acousto-structural coupled systems

摘要

In this study, modelling of the human hearing is considered. Due to the nonlinearity of the middle ear, the sound transfer changes as the equilibrium position of the middle ear structure varies. For the description of the middle ear a nonlinear elastic multibody system is derived. The tympanic membrane and the air in the ear canal as well as in the tympanic cavity are considered as elastic bodies. They are first modelled using the finite element method. The large number of degrees of freedom makes a following reduction step of the acousto-structural finite element model inevitable. The second-order structure of the system matrices is preserved by applying reduction techniques based on Petrov–Galerkin projection. The nonlinearity of the tympanic membrane is included following the approach of parametric model order reduction by matrix interpolation assuming that the nonlinearity can be represented by the relative pressure between the ear canal and the tympanic cavity. Finally the static and dynamic behaviour of the simulation model is reviewed for different static pressure loads of the middle ear.