Generation of a Virtual Speaker and Baffle on a Thin Plate Controlled by an Actuator Array at the Boundary

The pattern of bending vibration on a thin plate is controlled to create a virtual speaker and baffle set. An actuator array at the plate edges is used to generate the bending wave to form the desired vibration pattern. The speaker zone is rendered to maintain a uniform phase as a speaker, whilst the rest of the plate is kept to be tranquil to serve as a baffle. From the rendering information and the potential positions of the actuators, the actuator gains are determined in an inverse manner. Vibration on a finite plate is modeled by the superposition of Green's functions between the actuators and field points, which depend on the speaker size and location, and the shape and material of plates. Parametric studies are conducted to determine the effect of those functions on the radiated sound characteristics. Simulation results show that the radiated sound spectrum features similar dips at some Helmholtz numbers would cause the deterioration of sound quality and reproducibility. These dips appear because of two typical reasons. The first condition is that the Helmholtz number becomes about 3.8 and 7.0, corresponding to the low-order radial modes of the circular speaker zone having circumferential nodes. The other arises when the distance between the speaker center and the plate edges is an integer multiple of the bending wavelength. The proposed method is tested on the roof panel of a car to compensate for the poor response of the built-in speakers. It is shown that the virtual speaker has a uniform phase in the speaker zone and that the low-frequency performance is reinforced well.