Lightweight sound insulation optimization of simply supported locally resonant plate

Abstract

A theoretical model of the normal sound insulation of a rectangular locally resonant (LR) plate with simply supported boundary conditions is established. The accuracy of the model is verified through comparison with finite element simulation results. Considering a 1-m² aluminum plate as the research object, a non-dominated genetic algorithm is introduced. The algorithm optimizes the lightweight sound insulation of an LR finite plate with a center frequency band of 20–800 Hz as the optimization objective of maximum average sound insulation and minimum mass. The optimization parameters are substrate thickness and local resonance parameters (including resonator target frequency (f_obj), number of resonators, additional mass ratio, and resonator damping). Optimization results indicate that the average sound insulation fluctuates at approximately 2 dB due to changes in f_obj. The results also provide an optimal solution to the algorithm. The optimal sound insulation value curve of LR plates corresponding to different surface densities of intermediate improved cases is fitted and compared with the sound insulation value of an equal-mass bare plate. Under lightweight optimization, the resonators are deemed capable of improving the local frequency band sound insulation. In contrast, the wideband average sound insulation can approximate but not surpass the insulation provided by the equal-mass bare plate. In practical applications, an LR plate that can improve the local frequency band sound insulation and ensure the overall lightweight sound insulation performance of the wide frequency band can be obtained. This can be achieved by analyzing the frequency spectrum of optimal points in the lightweight sound insulation optimization process. Relevant research can provide a basis for the evaluation and design of the low-frequency sound insulation of plates for transportation equipment, such as airplanes, high-speed trains, and cars.