Abstract In this study, band gaps of SH-waves (horizontally polarized shear waves) propagating in a thermal-sensitive viscoelastic matrix are investigated. Metallic films acting as heat sources are periodically embedded into the matrix, which establishes a periodically inhomogeneous thermal field. The homogenous matrix is therefore transformed into functionally gradient phononic crystals (PCs). A three-parameter solid model is employed to describe the viscoelasticity of the present matrix. By virtue of a transfer matrix method incorporated within a laminated model, the dispersion equation of SH-waves is finally obtained, from which the band gaps are determined. The transmission spectra of a finite-periodic PC are also solved to validate the band gaps. In numerical examples, the influences of incident angles of SH-waves and viscoelasticity of matrix on band gaps are discussed first. Then the research focuses on the means to tune the band gaps by manipulating the inputted powers of heat sources. Numerical examples demonstrate that such a strategy is effective and convenient in tuning the positions and widths of band gaps. A viscous parameter, i.e., the ratio of initial-state to final-state storage moduli, significantly affects the band locations and bandwidths, while the locations of low-order band gaps hardly move with the incident angle of SH-waves. Band gaps of several orders are expected to locate in lower-frequency domain, and the total bandwidth becomes larger as the inputted heat flux increases. This paper lays theoretical foundation to manufacture viscoelastic functionally graded PCs which can be used in frequency-selective devices. Graphical abstract

中文翻译：

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粘弹性功能梯度声子晶体的带隙操纵

摘要 在这项研究中，研究了在热敏粘弹性基质中传播的 SH 波（水平极化剪切波）的带隙。作为热源的金属薄膜周期性地嵌入基体中，从而建立了周期性的非均匀热场。因此，同质矩阵转化为功能梯度声子晶体 (PC)。采用三参数实体模型来描述当前基体的粘弹性。通过层合模型中的传递矩阵方法，最终得到SH波的色散方程，由此确定带隙。还求解了有限周期 PC 的透射光谱以验证带隙。在数值例子中，首先讨论了SH波入射角和基体粘弹性对带隙的影响。然后研究重点是通过操纵热源输入功率来调整带隙的方法。数值例子表明，这种策略在调整带隙的位置和宽度方面是有效和方便的。粘性参数，即初态与终态存储模量的比值，显着影响带位置和带宽，而低阶带隙的位置几乎不随 SH 波的入射角移动。预计几个数量级的带隙位于低频域，并且总带宽随着输入热通量的增加而变大。本文为制备可用于频率选择器件的粘弹性功能梯度PC奠定了理论基础。图形概要