A complete vibroacoustic model for the nonlinear response of imperfect circular plates: Application to sound synthesis

A complete vibroacoustic model is presented in order to compute numerically the sound pressure generated by a thin circular plate vibrating with large amplitude motions. The vibratory part relies on a modal approach for the von Kármán thin plate equations. A special emphasis is put in this paper on the inclusion of a geometrical imperfection describing the shape of the circular plate, hence extending previous results for perfect plates to the generic case of imperfect plates and shallow shells. A conservative scheme is used in order to integrate in time the modal equations of motion for the imperfect plate. The acoustic radiation is taken into account by using a finite difference approach for the sound field. The vibroacoustic coupling gives rise to a complete model which is applied for the purpose of sound synthesis of cymbals and gong-like instruments. Simulation results are shown in order to investigate the influence of the geometric imperfection on the sound produced. Plates with different profiles are compared and focus is set on the ability of the imperfection to favour the appearance of the turbulent regime.