In order to solve the problem of low-frequency noise of aircraft cabins, this paper presents a new Helmholtz type phononic crystal with a two-dimensional symmetric structure. Under the condition of the lattice constant of 62 mm, the lower limit of the first band gap is about 12 Hz, and the width is more than 10 Hz, thus the symmetric structure has distinct sound insulation ability in the low-frequency range. Firstly, the cause of the low-frequency band gap is analyzed by using the sound pressure field, and the range of band gaps is calculated by using the finite element method and the spring-oscillator model. Although the research shows that the finite element calculation results are basically consistent with the theoretical calculation, there are still some errors, and the reasons for the errors are analyzed. Secondly, the finite element method and equivalent model method are used to explore the influence of parameters of the symmetric structure on the first band gap. The result shows that the upper limit of the first band gap decreases with the increase of the lattice constant and the wedge height and increases with the increase of the length of wedge base; the lower limit of the band gap decreases with the increase of the wedge height and length of wedge base and is independent of the change of lattice constant, which further reveals the essence of the band gap formation and verifies the accuracy of the equivalent model. This study provides some theoretical support for low-frequency noise control and broadens the design idea of symmetric phononic crystal.

中文翻译：

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一种新型亥姆霍兹型声子晶体的低频带隙特性研究

为了解决飞机机舱低频噪声问题，本文提出了一种新型的二维对称结构亥姆霍兹型声子晶体。在晶格常数为62mm的条件下，第一带隙下限约为12Hz，宽度大于10Hz，因此对称结构在低频范围内具有明显的隔声能力。首先利用声压场分析了低频带隙产生的原因，并利用有限元方法和弹簧振子模型计算了带隙范围。虽然研究表明有限元计算结果与理论计算基本一致，但仍存在一定的误差，分析了产生误差的原因。第二，采用有限元法和等效模型法探讨了对称结构参数对第一带隙的影响。结果表明，第一带隙的上限随着晶格常数和楔高的增加而减小，随着楔底长度的增加而增加；带隙下限随着楔高和楔底长度的增加而减小，且与晶格常数的变化无关，进一步揭示了带隙形成的本质，验证了等效模型的准确性。该研究为低频噪声控制提供了一定的理论支持，拓宽了对称声子晶体的设计思路。