Dynamics and Waves in Loudspeaker Cones

Several analytic and numerical models have been proposed to study the dynamic behaviour of loudspeaker cones, generally based on thin shell elements. The purpose of this paper is to link together some of these models by decomposing the results of a finite element analysis in terms of wave components. This is achieved using the wave finite element, WFE, method. A full finite element model is constructed first and the forced responses of the loudspeaker at different frequencies are calculated. Then, a wave finite element analysis is used to calculate the wave properties of the loudspeaker cone, in terms of wave mode-shape and wavenumber, as a function of position. Using these to decompose the overall results from the finite element analysis, the responses of the loudspeaker cone can be interpreted in terms of wave propagation. It is shown how the loudspeaker cone moves as a rigid body, due to in-plane waves, at low frequencies. As the excitation frequency increases, the transverse velocity of the cone surface becomes non-uniform, since the amplitude of the vibration increases towards the base of the cone, where bending waves can propagate. The transition point moves towards the apex of the cone with increasing excitation frequency until at high enough frequencies the whole cone is dominated by bending waves.