Abstract Metamaterial with various degrees of bandgap tunability is an emerging area in manipulating elastic wave transmission characteristics for next generation phononic devices. Although several attempts are made employing multi-fields such as magnetic, electric and thermal etc., mechanical deformation based tunable bandgap is a major interest. However, achieving tunability in terms of broadening or terminating the bandgap in locally resonant acoustic metamaterial (LRAM) remains as challenging tasks. In this work, we propose LRAM by integrating a two-dimensionally periodically arranged square unit cells consisting of soft coated hard inclusion embedded in a polymer scaffold. We develop computational framework to simulate the low frequency bandgap of unit cell under external deformation. At first quasi-static analysis of unit cell has been performed to find static displacement field under prescribed deformation. Further, utilizing Bloch-Floquet wave analysis for the periodic unit cell and finite element based numerical scheme, an eigenvalue problem is formulated to predict dispersion response within irreducible Brillouin zone (IBZ). Analyzing the symmetry group of the unit cell under deformed state for a series of loading, we extract the bandgap responses. Moreover, we illustrate tunable bandgap at low frequency regimes for different inclusion shapes and sizes. To correlate extension and suppression of bandgap under the applied deformation, evolution of local resonances are described with vibration mode shapes.

中文翻译：

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解开外加变形下多相超材料中可调低频带隙共振的相互作用

摘要 具有不同带隙可调性的超材料是控制下一代声子器件弹性波传输特性的新兴领域。尽管使用多场如磁、电和热等进行了多次尝试，但基于机械变形的可调带隙是主要的兴趣。然而，在局部共振声学超材料 (LRAM) 中扩大或终止带隙方面实现可调谐性仍然是一项具有挑战性的任务。在这项工作中，我们通过集成由嵌入聚合物支架中的软涂层硬夹杂物组成的二维周期性排列的方形晶胞来提出 LRAM。我们开发了计算框架来模拟外部变形下晶胞的低频带隙。首先进行了晶胞的准静态分析，以找到规定变形下的静态位移场。此外，利用周期性晶胞的 Bloch-Floquet 波分析和基于有限元的数值方案，制定了特征值问题来预测不可约布里渊区 (IBZ) 内的色散响应。分析一系列加载变形状态下晶胞的对称群，我们提取带隙响应。此外，我们说明了不同夹杂物形状和尺寸在低频范围内的可调带隙。为了将施加变形下带隙的扩展和抑制相关联，用振动模式形状描述了局部共振的演变。利用周期性晶胞的 Bloch-Floquet 波分析和基于有限元的数值方案，制定了一个特征值问题来预测不可约布里渊区 (IBZ) 内的色散响应。分析一系列加载变形状态下晶胞的对称群，我们提取带隙响应。此外，我们说明了不同夹杂物形状和尺寸在低频范围内的可调带隙。为了将施加变形下带隙的扩展和抑制相关联，用振动模式形状描述局部共振的演变。利用周期性晶胞的 Bloch-Floquet 波分析和基于有限元的数值方案，制定了一个特征值问题来预测不可约布里渊区 (IBZ) 内的色散响应。分析一系列加载变形状态下晶胞的对称群，我们提取带隙响应。此外，我们说明了不同夹杂物形状和尺寸在低频范围内的可调带隙。为了将施加变形下带隙的扩展和抑制相关联，用振动模式形状描述局部共振的演变。分析一系列加载变形状态下晶胞的对称群，我们提取带隙响应。此外，我们说明了不同夹杂物形状和尺寸在低频范围内的可调带隙。为了将施加变形下带隙的扩展和抑制相关联，用振动模式形状描述局部共振的演变。分析一系列加载变形状态下晶胞的对称群，我们提取带隙响应。此外，我们说明了不同夹杂物形状和尺寸在低频范围内的可调带隙。为了将施加变形下带隙的扩展和抑制相关联，用振动模式形状描述局部共振的演变。