Theoretical and experimental investigation on the low-frequency vibro-acoustic characteristics of a finite locally resonant plate

This study investigates the low-frequency vibro-acoustic characteristics of a finite locally resonant (LR) plate. A dynamic model of the finite LR plate consisting of periodic arrays of beam-like resonators attached to a thin aluminum plate with simply supported boundary conditions is established, and the average vibration response and radiated efficiency are theoretically determined by using modal-superposition and harmonic-balance methods. In addition, the study investigates the influence of the parameters and number of additional resonators on the vibro-acoustic performance of the finite LR plate. Finally, a vibration experiment of a finite plate with 8 x 10 uniformly distributed beam-like resonators validates the theoretical analysis results. The numerical and experimental results show that the finite LR plate has a low-frequency bandgap that can suppress the vibration and radiated noise of the structure, and the bandgap position is close to the resonance frequency of resonators. The position and performance of bandgaps can be influenced by changing the parameters and number of resonators. The experimental results show a bandgap ranging from 370 to 425 Hz, which is consistent with the theoretical prediction. The finite LR plates proposed in this study can find potential applications in the attenuation of low-frequency vibration and noise.