Finite element simulation of an axisymmetric acoustic transmission system with a sound absorbing wall

A finite element formulation for the axisymmetric acoustic field problem with an arbitrary sound absorbing wall is developed on the true adjoint system approach. A triangular ring element with a second order polynomial trial function is used for discretization. As a first numerical example, the transmission characteristic of acoustic filters of expansion type is considered, in which the wall is partly treated with sound absorbing material. As a second example the effect of a temperature gradient in the chamber on the transmission characteristic is calculated. The third example is the calculation of the throat impedance of conical and exponential acoustic horns, for which the half sphere into which the radiation travels is assumed to be terminated at an appropriate radius by a hypothetical wall having the characteristic impedance of the acoustic medium. The calculated results are verified by comparison with measured results.