薄膜与Helmholtz腔耦合结构低频带隙  

Low frequency band gaps of Helmholtz resonator coupled with membrane

作　　者：陈鑫[1] 姚宏[1] 赵静波[1] 张帅 贺子厚 蒋娟娜 Chen Xin;Yao Hong;Zhao Jing-Bo;Zhang Shuai;He Zi-Hou;Jiang Juan-Na(Department of Basic Sciences,Air Force Engineering University,Xi’an 710051,China)

机构地区：[1]空军工程大学基础部

出　　处：《物理学报》2019年第21期120-129,共10页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:11504429)资助的课题~~

摘　　要：设计了一种含薄膜壁的Helmholtz型声子晶体,该结构利用了空气和薄膜的耦合振动,一方面将刚性壁转变为柔性壁,降低了一阶振动时的等效刚度,使第一带隙下限分别低于同参数下的普通Helmholtz型声子晶体和薄膜,另一方面基于局域共振原理,由于薄膜的出现和腔口空气通道长度的增加,使得结构在低频范围内存在多个振动模态,从而将原有一个带隙扩展为多个带隙.将该结构带隙上下限分别等效为环形系统和串联系统,用传递矩阵法和有限元法两种方法计算了其低频带隙范围,两种方法结果吻合良好.通过调整参数对带隙调控规律进行了进一步分析,结果显示,在低频范围内,既可以通过改变与腔口空气通道或薄膜相关的参数,在保证其中某些带隙变化不大的情况下,单独调整其他带隙;也可以通过调整内外腔体积,对所有带隙进行调控.In this paper, a phononic crystal is designed using a Helmholtz resonator with a membrane wall, in which the coupled vibration of air and membrane is utilized. The structure of the Helmholtz resonator is a twodimensional structure. On the basis of the square Helmholtz resonator, a "W"-type outlet is used as a cavity outlet to increase the air quality involved in resonance, and the cavity wall is replaced with a membrane with distribution mass to increase the number of resonance units.The finite element method is used to calculate the band gaps and transmission loss of sound below 1700 Hz.The results show that the starting frequency of the first band gap of the structure is further reduced. At the same time, it is lower than the starting frequency of ordinary Helmholtz structure and the natural frequency of membrane under the same conditions. Then, a new peak of transmission loss is obtained, and its value is greater than the original structure’s. And although the width of the first band gap is reduced, some new band gaps appear in the low-frequency range, so that the total band gap width is improved.By analyzing the vibration mode of the membrane and sound pressure distribution, it is found that the sum of the sound pressures of the outer cavity is zero at the starting frequencies of the band gaps, and the sound pressure of the inner and outer cavity are respectively positive and negative at the cut-off frequency. With the increase of frequency, the vibration mode of the membrane gradually turns from low-order to high-order, but no anti-symmetric-type mode participation is found at the starting and cut-off frequency.The components of the structure can be made equivalent to corresponding ones, respectively, i.e. air in the outlet is equivalent to uniform flexible rod, and the air in the inner and outer cavity are equivalent to a spring.So that the structure can be equivalent to a series system consisting of a rod, a spring and a membrane at starting frequency of the band gap, and a loop system consisting of a ro

关 键 词：Helmholtz共振腔 低频带隙 噪声控制 声子晶体 

分 类 号：O735[理学—晶体学]