The recently demonstrated 'modal crossover network' method for flat panel loudspeaker tuning employs an array of force drivers to selectively excite one or more panel bending modes from a spectrum of panel bending modes. A regularly spaced grid of drivers is a logical configuration for a two-dimensional driver array, and although this can be effective for exciting multiple panel modes it will not necessarily exhibit strong coupling to all of the modes within a given band of frequencies. In this paper a method is described to find optimal force driver array layouts to enable control of all the panel bending modes within a given frequency band. The optimization is carried out both for dynamic force actuators, treated as point forces, and for piezoelectric patch actuators. The optimized array layouts achieve similar maximum mode coupling efficiencies in comparison with regularly spaced driver arrays; however, in the optimized arrays all of the modes within a specified frequency band may be independently addressed, which is important for achieving a desired loudspeaker frequency response. Experiments on flat panel loudspeakers with optimized force actuator array layouts show that each of the panel modes within a selected frequency band may be addressed independently and that the inter-modal crosstalk is typically −30 dB or less with non-ideal drivers.
Previous publications on flat-panel, or distributed-mode, loudspeakers generally assume that a localized driving force is able to spread energy evenly across the surface of a panel. However, investigations have shown that panel vibrations remain localized around the driving point at high frequencies, and this paper presents a deeper investigation into this phenomenon. Energy spreading will only occur when the panel is actuated in a frequency region with a low density of modes, as many modes actuated together will combine to form a band-limited delta function at the location of the driving force. A quantitative measure of localization is introduced, based on the ratio of the energy contained in a small region around the driving point to the energy contained in the entire panel. Simulations demonstrate that the frequency cutoff for localized vibrational behavior is dependent on the damping rate of the modes and the location of the driver. Experiments validate this theory by analyzing the vibrational behavior of a plate subject to small inertial drivers at various locations with a laser vibrometer.
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