Dynamic Modeling and Modal Analysis of Rectangular Plates with Edge Symmetric Periodic Acoustic Black Holes

The vibration noise of plate structures in engineering is strongly related to the modal resonance, and modal design is the key to improve the dynamic characteristics of plate structures and avoid structural resonance. This paper investigates the dynamic and mode characteristics for an edge periodic acoustic black hole plate structure to provide a new approach to vibration and sound attenuation in plate structures. Firstly, based on the principles of symmetry and periodicity, this work presents the geometrical modeling and mathematical description of a rectangular plate with symmetrical periodic acoustic black holes at its edge. Then, it presents the dynamic modeling of a rectangular plate with periodic acoustic black holes at its edge via the “remove-and-fill” substitution method, which reveals the effects of the structural parameters and period distribution, etc., on the modal characteristics of vibration. The study indicates that the power law index, radius, number and configuration (e.g., semicircular, rectangular block shape) of the edge periodic acoustic black holes significantly affect the modal frequency of the rectangular plate, and increasing the radius of the acoustic black holes or the number of the black holes results in a decrease in the modal frequency of the rectangular plate. Moreover, the four-side symmetric layout achieves broader modal frequency modulation, while semicircular acoustic black holes can achieve a lower modal frequency compared with the rectangular wedge-shaped acoustic black hole. The theoretical model is verified by finite element simulation (FEM) and experiments, in which the errors of the first six modal frequencies are within 2%. The research in this paper provides a theoretical basis for the realization of modal frequency control in plate structures and the suppression of structural resonance through the design of edge periodic acoustic black hole structures.