A robust inverse method for the complex wavenumber space (complex k-space) extraction is essential for structural vibration and damping analysis of two-dimensional structures. Most existing methods suffer from extracting the reliable complex k-space of plates in the presence of realistic uncertainties, especially for plates with low damping properties. To this end, this paper presents a new method for extracting the dispersion and damping characteristics of two-dimensional periodic structures using only the full-field displacement fields as input. The proposed method, the Algebraic K-Space Identification 2D technique (AKSI 2D), is an extension of the Algebraic Wavenumber Identification technique to solve two-dimensional problems. The optimised formulas are developed within the algebraic identification framework, which allows the extraction of all the properties of the complex k-space in a comprehensive way. The proposed method is validated numerically and experimentally, and its performances are compared with other popular k-space identification methods under different uncertainty conditions. The test cases cover analytically solved isotropic fields to numerically solve orthotropic fields and finally experimental measurements. The different cases show promising results and demonstrate that the proposed method is a robust tool to characterise the wave propagation of two-dimensional structures under stochastic structural and constitution conditions.

中文翻译：

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代数 K 空间识别 2D 技术，用于在存在不确定性的情况下自动提取 2D 结构的复杂 k 空间


用于复波数空间（复k空间）提取的稳健逆方法对于二维结构的结构振动和阻尼分析至关重要。大多数现有方法在存在现实不确定性的情况下提取可靠的板的复杂 k 空间，特别是对于具有低阻尼特性的板。为此，本文提出了一种仅使用全场位移场作为输入来提取二维周期性结构的色散和阻尼特性的新方法。所提出的方法，代数 K 空间识别二维技术（AKSI 2D），是代数波数识别技术的扩展，用于解决二维问题。优化公式是在代数辨识框架内开发的，可以全面提取复杂k空间的所有属性。该方法经过数值和实验验证，并在不同不确定性条件下与其他流行的 k 空间识别方法进行了性能比较。测试用例涵盖解析求解的各向同性场、数值求解正交各向异性场以及最终的实验测量。不同的案例显示了有希望的结果，并证明所提出的方法是表征随机结构和构成条件下二维结构的波传播的强大工具。