Comprehensive analysis of band gap of phononic crystal structure and objective optimization based on genetic algorithm

In this paper, a type of acoustic metamaterial structure is proposed, which provides a new idea for the structural design of metamaterials with specific wave propagation direction. The structure is named snowflake-like square phonon crystal structure (SLS). Firstly, based on Bloch theorem and finite element method, the energy band curve of the structure is obtained, and the low frequency band gap in the range of 300–600Hz is obtained, and the band gap is analyzed comprehensively with the main band gap. It includes the vibration modal analysis at the corresponding point of the boundary of Brillouin zone and the establishment of a corresponding simplified model to explain the mechanism of band gap opening and closing more deeply. At the same time, the band gap characteristic of SLS structure is verified by the transmission curve, and the difference of elastic wave transmission results between inside and outside the band gap is given. Not only that, the real propagation direction of the band gap is described by group velocity and equal frequency diagram. The results show that in the range of relatively low frequency elastic waves, the propagation of elastic waves in the structure has a certain direction and region, that is, the structure can play a good effect of vibration and noise reduction. In addition, after the comprehensive analysis, this paper analyzes the influence trend of various factors on the band gap of the structure, and establishes the optimization model of the target band gap based on genetic algorithm, and finally obtains the optimized SLS structure. The results show that the band gap width is more than 2.5 times larger than the initial band gap width. It shows that even under the specific structure, the optimization space of the band gap still has a high lifting upper limit.