Optimization Scheme Of Low-frequency Band Gaps For New Locally Resonat Phononic Crystal Structure

Acoustic functional materials——phononic crystals which have great potential for vibration attenuation and noise reduction due to the band gap property.The traditional Bragg phononic crystal has a high band gap and cannot meet the requirements of low-frequency vibration and noise suppression below 250 Hz in daily life.Because of the existence of a low-frequency resonance unit,the locally resonant phononic crystal can suppresses the elastic wave propagation in certain frequency bands,thereby obtaining low-frequency band gaps.When it was put forward,it received great attention and many phononic crystal structures emerged.However,to date,there has been little exploratory research in the optimization of the phononic crystal band gap.In this paper,we try to solve the above problems and carry out the research of low-frequency band gap optimization based on the new locally resonant phononic crystal structure,which provides a theoretical basis for the optimization of phononic crystal structure.Four novel locally resonant phononic crystal structures are proposed:comb,ring,spiral,and fan-like solid-liquid locally resonant phononic crystal structures.Firstly,the band structures of four phononic crystal structures are calculated by the finite element method.The results show that the band gaps of the four structures are in the lower frequency range.Secondly,in order to verify the correctness of the band structures,the transmission characteristics of the four structures are further calculated.The results show that the four locally resonant phononic crystal structures have significant attenuation effects on the elastic waves in the respective band gaps.Finally,the mechanisms of opening the low-frequency band gap of comb,ring and spiral phononic crystal structures are analyzed by the corresponding vibration modes and displacement at the upper and lower edges of the band gaps;And through the control variable method,we study the influence of the length of the scatterer on the band gaps of the fan-like solid-liquid phononic crystal structure.In order to further provide theoretical basis for the optimization of locally resonant phononic crystal structure,a general band gap optimization scheme is proposed and is applied to the comb,ring and spiral phononic crystal structure optimization design.Firstly,the influence of the key geometric parameters of the three structures on the respective band gaps is studied to determine their ideal ranges.Secondly,the multi-component numerical experiment scheme is designed by response surface method,and the functional relationships between keygeometric parameters and band gaps are obtained by using data processing software Design-expert.Thirdly,according to the application environment,the optimization model is established with the widest total band gaps as the target,and the optimized band gaps and corresponding geometric parameters are obtained by the interior point method.Finally,the optimized band gaps are verified by the finite element method.The results show that the optimization scheme has high accuracy and can be extended to the acoustic functional material structure optimization design.