A numerical model for axial strain vibrations of brass wind instrument bells

Experimental observations suggesting an effect of wall vibrations on the radiated sound of wind instruments have been published by many different authors over a very long period of time. In the case of brass wind instruments a theory which is consistent with experimental results has been developed rather recently. It suggests that axial strain vibrations of the bell are responsible for the observed interaction between structural vibrations and the radiated sound. In this paper a numerical model of such axial vibrations in brass wind instrument bells is proposed, which is computationally much less expensive than Finite Element Method (FEM) simulations but comparably accurate. It takes advantage of the relatively simple axisymmetric and thin-walled structure of bells and the knowledge that several degrees of freedom can be neglected in that particular problem. The proposed model is based on a frequency domain approach published by Kausel et al. in JASA 137(6) where the bell’s mass and stiffness is represent...