Transient modal radiation of axisymmetric sources: application to loudspeakers

For high amplitudes of vibrations, loudspeakers are subject to nonlinear phenomena that are responsible for audible distortions. In order to describe the complex dynamics of the system, the displacement field as well as the radiated sound pressure must be expressed in the time-domain. Thus the present study proposes a transient model of the acoustic radiation of axisymmetric structures. The pressure field is approximated by the Rayleigh integral corresponding to a monopole source distribution over the non-planar vibrating surface. The displacement field is expanded on the linear modes of the structure and a change of variables in the Rayleigh integral is then proposed in the case of a monotonic profile function to compute the Spatial Impulse Response associated to each mode of vibration efficiently. The results are compared to the formulation obtained in the case of planar and spherical sources. The method of calculation is then derived in the case of a typical loudspeaker profile (association of a truncated cone with a spherical cap). Finally, the present approach is used to estimate the nonlinear radiation pattern of a prototype loudspeaker and predictions are compared to measurements in anechoic room.