Low frequency band gap characteristics of double-split Helmholtz locally resonant periodic structures

Abstract

A double-split Helmholtz periodic structure with the characteristic of local resonance is designed and constructed in this paper. The double-split periodic structural cell which can be divided into internal and external cavities is adopted in structure. In such a kind of structure, the resonating area is remarkably expanded while the inner cavity is continuously enlarged. Thus, a satisfactory feature of low frequency resonance can be obtained. At the same time, the adjustability of band gap is achieved by the designed adjustment of the arc length of the inner cavity, therefore, the effect of sound insulation in a specific low frequency band can be achieved. In the analyses of the mechanism and factors of the generation of low frequency band gap, the mathematical model of the upper and lower limits of the band gap is established by using the electric circuit analogy. And some comparative analyses between the methods of electric circuit analogy and finite element method are carried out. The result suggests that a satisfactory feature of low frequency band gap is presented, and the first band-gap ranges from 86.9 Hz to 138.2 Hz. The low frequency band gap can be influenced by the arc length of inner cavity, the space between inner and outer cavities, and the interaction of the structural cells in the periodic arrangement. The longer the arc length of the inner cavity, the lower the low frequency band gap will be; the longer the distance between inner and outer cavities, and the higher the frequency of band gap, the worse the low frequency effect will be; the lower limit of low frequency band gap cannot be influenced by reducing the space between individual structures, on the contrary, the width of low frequency band gap can be sharply increased. Plenty of practical and theoretical support in the field of low frequency noise reduction is offered in the research.