Topological design of square lattice structure for broad and multiple band gaps in low-frequency range

Abstract

Several studies have demonstrated that the design of square lattice is an efficient approach to obtain band gap characteristics. However, there are still some challenges in the design of phononic crystals capable to prohibit the propagation of low-frequency waves. In the present paper, aiming to broaden and manipulate the low frequency band gaps, an innovative structure with filling materials in a square lattice is proposed, where the spatial distribution of the materials has been optimized using an improved genetic algorithm. By analyzing the band structure and vibration modes of the designed structure, it becomes evident that the low-frequency band gaps are obtained due to the local resonance of the constituent materials. The transmission spectrum of the finite designed structure confirms an efficient wave attenuation performance in the low-frequency range. Furthermore, the effect of ligament thickness on band gaps was also investigated. The designed phononic porous plate, featuring prominent band gap properties, can be used as an example to guide the topological design of phononic crystal structures for a wide range of engineering implementations.