Optimizing a distribution of resonators on a thin plate for the desired sound radiation

The periodic distribution of mechanical resonators on a thin plate has been studied to improve panel loudspeakers by exploiting the band gap phenomenon (BG), effectively forbidding vibrational modes in certain frequency ranges. Here, we present an optimization procedure to determine the distribution with a minimized number of resonators while achieving the desired sound radiation. A thin aluminum plate with periodic resonators is considered to open a BG from 355 Hz to 710 Hz, which covers an octave band. The structure is modeled using the finite element method. Each resonator is parameterized with a topological design variable, which represents the absence and presence of the resonator. Numerical examples are presented to demonstrate the optimization for the design of a defect and removing ineffective resonators to obtain the desired sound radiation. Experimental validations show good agreement with the numerical results in terms of spectral smoothness and spatial uniformity of sound radiation. In this case, the overall SPL is amplified by 10 dB, and the standard deviation is reduced by 5 dB by comparison with a bare plate.