The principal goal of this work was to develop a numerical method to study the coupling between internal and external fluid of a resonator, notably to study the link between the shape of a finite length resonator and his radiation. For this we study complex resonances, corresponding to the poles of the Green's function of system coupled with the external environment. The imaginary part of resonance frequencies is here directly related to losses due to radiation. We based our work on three main areas: an analytical study using a modal theory with the inclusion of non-planar modes, the development of a numerical method based on boundary finite elements and an experimental comparison of our theoretical results. The analytical modal theory has allowed us to study the radiation of finite length cylindrical pipe opening into an infinite screen, which is a reference case for further study. The numerical method, developed in a Fortran parallelized code, gave us the opportunity to study resonators with more complex geometries such as horns. To reduce computation time, we introduced an hybrid method mixing modal theory to describe the conservative part of system, that allows fast computation, and boundary element method, allowing a fine representation of complex geometries, to describe the radiating part. We have finished this work with a first experimental validation of results.
Relation between the shape and radiation of a finite length resonator. Numerical and experimental study of his complex resonances.