Abstract The application of shift cell technique is presented and discussed for periodic porous media described with equivalent fluid models: as it can be found in literature, it consists in a reformulation of classical Floquet-Bloch (F-B) conditions, in which the phase shift of the boundary conditions, related to wave propagation, is integrated into the partial derivative operator. Consequently, the periodicity is included in the overall behavior of the structure, while continuity conditions are imposed at the edges of the unit cell. Its major advantage stands in allowing the introduction of a generic frequency dependence of porous material behavior, through the resolution a quadratic eigenvalue problem, providing an efficient way to compute the dispersion curves of a porous material modeled as an equivalent fluid. A validation and a computational cost comparison are performed between the shift cell technique and the classical F-B approach, pointing out that the first can provide, among its other advantages, a sensible computational time reduction for this kind of analyses. The derivation of the equivalent acoustic properties of the unit cell from its dispersion characteristics is also investigated. To this aim, group velocity matrix formulation and a branch-tracking algorithm are described. Some test cases are used for validating the proposed methodology.

中文翻译：

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计算作为等效流体建模的周期性多孔材料的色散图

摘要 提出并讨论了位移单元技术在用等效流体模型描述的周期性多孔介质中的应用：如文献中所见，它包括经典 Floquet-Bloch (FB) 条件的重新表述，其中与波传播相关的边界条件被整合到偏导数算子中。因此，周期性包含在结构的整体行为中，而连续性条件则强加于晶胞的边缘。它的主要优势在于允许引入多孔材料行为的通用频率相关性，通过解决二次特征值问题，提供一种有效的方法来计算建模为等效流体的多孔材料的色散曲线。在移位单元技术和经典 FB 方法之间进行了验证和计算成本比较，指出第一种方法可以为此类分析提供合理的计算时间减少等优点。还研究了从其色散特性推导出晶胞等效声学特性的方法。为此，描述了群速度矩阵公式和分支跟踪算法。一些测试用例用于验证所提出的方法。还研究了从其色散特性推导出晶胞等效声学特性的方法。为此，描述了群速度矩阵公式和分支跟踪算法。一些测试用例用于验证所提出的方法。还研究了从其色散特性推导出晶胞等效声学特性的方法。为此，描述了群速度矩阵公式和分支跟踪算法。一些测试用例用于验证所提出的方法。