Abstract The dynamic behaviour of periodic thermodiffusive multi-layered media excited by harmonic oscillations is studied. In the framework of linear thermodiffusive elasticity, periodic laminates, whose elementary cell is composed by an arbitrary number of layers, are considered. The generalized Floquet-Bloch conditions are imposed, and the universal dispersion relation of the composite is obtained by means of an approach based on the formal solution for a single layer together with the transfer matrix method. The eigenvalue problem associated with the dispersion equation is solved by means of an analytical procedure based on the symplecticity properties of the transfer matrix to which corresponds a palindromic characteristic polynomial, and the frequency band structure associated to wave propagating inside the medium are finally derived. The proposed approach is tested through illustrative examples where thermodiffusive multilayered structures of interest for renewable energy devices fabrication are analyzed. The effects of thermodiffusion coupling on both the propagation and attenuation of Bloch waves in these systems are investigated in detail.

中文翻译：

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周期性热扩散层状材料的广义 Floquet-Bloch 谱

摘要 研究了谐波振荡激发的周期性热扩散多层介质的动力学行为。在线性热扩散弹性的框架中，考虑了周期性层压板，其基本单元由任意数量的层组成。施加广义Floquet-Bloch条件，通过基于单层形式解的方法结合传递矩阵法得到复合材料的普适色散关系。与色散方程相关的特征值问题通过基于回文特征多项式对应的传递矩阵的辛性特性的解析程序求解，最终推导出与波在介质内传播相关的频带结构。所提出的方法通过说明性示例进行测试，其中分析了对可再生能源设备制造感兴趣的热扩散多层结构。详细研究了热扩散耦合对这些系统中布洛赫波的传播和衰减的影响。