Locally resonant phononic crystal (LRPC) has the extraordinary property to prohibit the wave propagation in specific low-frequency ranges, however it exists limitation in engineering application due to narrow band gap width. Extensive achievements have been obtained on the locally resonant band gap (LRBG) tunability, whereas existing investigations mainly concern the independent primitive cells structure, which have the limitation in obtaining low-frequency and broadband simultaneously. In this paper, the composited locally resonant phononic crystals (CLRPC) are proposed and the effects of primitive cells contact state on the LRBG properties are investigated. The dispersion curves are applied to obtain the LRBG, and the corresponding modal features are analyzed to explain the band gap formation mechanism. The band structure indicates the design of composite primitive cells is able to increase the band gap number and obtain lower band gap, which is verified by the frequency response function (FRF). For the band gap formation mechanism, the asymmetric vibration due to primitive cells contact leads to diverse and strong coupling response, which generates more band gaps and reduces the band gap starting frequency, therefore the band gaps can be tuned by designing carefully the geometry structure of CLRPC. Further researches on band gap optimization demonstrate that the smaller cell spacing, smaller lattice constant and larger damping of coating layer should be satisfied to obtain broader LRBG and considerable attenuation synchronously. This investigation can provide references for the locally resonant isolation structure design in the low-frequency vibration control field.

中文翻译：

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复合基元对局部共振声子晶体带隙特性的影响

局部共振声子晶体（LRPC）具有抑制特定低频范围内波传播的非凡特性，但由于窄带隙宽度在工程应用中存在限制。在局部谐振带隙（LRBG）可调性方面已经取得了广泛的成果，而现有的研究主要涉及独立的原始单元结构，其在同时获得低频和宽带方面存在局限性。在本文中，提出了复合局部共振声子晶体（CLRPC），并研究了原始细胞接触状态对LRBG特性的影响。应用频散曲线获得LRBG，并分析相应的模态特征来解释带隙形成机制。能带结构表明复合原始单元的设计能够增加带隙数并获得较低的带隙，这由频率响应函数（FRF）验证。对于带隙形成机制，由于原始细胞接触引起的不对称振动导致多样且强烈的耦合响应，从而产生更多的带隙并降低带隙起始频率，因此可以通过精心设计的几何结构来调整带隙。 CLRPC。对带隙优化的进一步研究表明，需要满足更小的单元间距、更小的晶格常数和更大的涂层阻尼，才能同时获得更宽的LRBG和相当大的衰减。