| Acoustic metamaterial is a kind of periodical artificially sub-wavelength materials or structure, which has many acoustic properties that don’t exist in traditional materials, such as: negative mass density and negative bulk module. Thus, acoustic metamaterial has great application value in reducing noise and improving the environment. The width of band gaps of many previously studied structures is not wider enough to meet the requirement of sound insulation in low frequency range.This paper proposes a petal-shaped acoustic metamaterial with ultra-wide band gaps on the basis of acoustic metamaterials’ band structure theory and band gap’s theory.Band structures of the two kind of petal-shaped matamaterials are calculated and comparatively analyzed by numerical simulations based on finite element method(FEM). Finally, the experiment based on the four-microphone transfer matrix method is operated to measure the sound transmission character of the designed structure, the results of calculation by FEM and measurement in the experiment are compared and analyzed. The paper’s detailed content is as following:(1) The model of petal-shaped acoustic metamaterials is built and optimized,and band structures of designed structures are calculated. Compared with other previously studied acoustic metamaterials, this kind of material has an advantage:wider complete band gaps. It is suggested that the structure we designed can generate several complete band gaps through only one kind of unit and one layer rather than different unit and several layers. The structure is built based on local resonance which corresponds to the range of low frequency, so the lattice constant of the structure should be consistent with low-frequency band gaps.(2) The paper explains the mechanism of local resonance from unit’s vibration module shapes. The vibration of acoustic metamaterials unit is a kind of local resonance: Mode "1" has a translational motion in z direction, mode "2" and mode "3" have rotational motion with fixed axis in x-y plane. Mode "4" and mode "5" havetranslational motion in y direction and in x direction, respectively. For the mode "6", it vibrates rotational with fixed axis in z direction. Specially, in mode "7", only the "petal" component vibrates in x-y plane and the others remain static, which is quite different from the other modes.(3) Effects of geometrical parameters on band structures will provide effective evidence for designation of new structure. Making the structure with one petal as an example to study the effects of all kinds of parameters on boundaries of the three complete band gaps of structures. It is shown that the lattice constant, the radius of hemisphere and the thickness of silicone rubber plate are the main factors to affect the band structure of the unit. Yet, the effects of the number of the petal on the band gap is studies, and the unit with one petal has excellent band gaps.(4) The paper includes the experiment which based on the transfer-matrix four-microphone method. The results of calculation and experiment are compared and analyzed. It suggested that the curves of two results keep consistent in some frequency range.
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