Optimum placement of resonators on a thin panel for the spectrally smooth sound radiation

With excitations using electro-dynamic actuators, a panel itself can serve as a loudspeaker i.e., flat panel loudspeaker. For this application, the spectrally smooth sound radiation is desired, which is usually challenging due to the sparse vibrational modes. The method using periodically distributed resonators was studied in order to achieve the spectral smoothness by utilizing the band gap. Here, we extend the approach by using an optimization to place the resonators for the desired sound radiation. The contribution of resonators are parameterized with continuous design variables. An optimization problem, which minimizes the total number of resonators while constraining the desired sound pressure level (SPL), is considered. Numerical examples are presented to place the resonators on a thin aluminium panel. For this specific case, the standard deviation of the SPL decreases by 9 dB within frequencies between 355 Hz and 710 Hz.