Comparison of two vibro-acoustic inverse methods to radiate a uniform sound field from a plate

Abstract

The radiated sound from a conventional panel speaker, often excited by an actuator, is usually distorted due to the multi-modal response of the regular panel. To avoid such an acoustically disadvantageous feature of the conventional panel speakers, an array of actuators can be used for controlling the panel vibration to obtain the desired acoustic response. In this paper, two different control methods by using the actuator array are compared in the viewpoint of the solution stability, the input efficiency, and the acoustic performance, in particular at low frequencies rendered in a hemispherical uniform radiation. The indirect inverse rendering method is to create a vibration pattern composed of a virtual speaker and baffle, and the direct inverse rendering method controls the array actuators to form a spatial distribution of panel vibration to directly produce the uniform radiation field. The actuator positions are confined at the periphery of the plate, which are advantageous in exciting the multiple modes and saving the central zone covered by the plate for other purposes. Numerical simulations are conducted for a thin rectangular plate with simply supported boundary condition in the frequency range below 300 Hz. It is found that both rendering methods can produce the uniform hemispherical sound radiation field, but the rendering error is −20 dB for indirect method and −50 dB for direct method. The singularity problem due to the ill-conditioning of the system appears in the direct method. Effect of applying the regularization technique to obtain a stable solution is studied for the system contaminated with a large amount of noise. It is observed that the result of using the direct method becomes dramatically stable with a reduction of condition number from O (1017) to O (104). Also, the input gains of the actuator are reduced as much as 35 dB for both rendering methods.