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Estimating dispersion curves from Frequency Response Functions via Vector-Fitting

机译：通过矢量拟合从频率响应函数估计色散曲线

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摘要

Driven by the need for describing and understanding wave propagation in structural materials and components, several analytical, numerical, and experimental techniques have been developed to obtain dispersion curves. Accurate characterization of the structure (waveguide) under test is needed for analytical and numerical approaches. Experimental approaches, on the other hand, rely on analyzing waveforms as they propagate along the structure. Material inhomogeneity, reflections from boundaries, and the physical dimensions of the structure under test limit the frequency range over which dispersion curves can be measured. In this work, a new data-driven modeling approach for estimating dispersion curves is developed. This approach utilizes the relatively easy-to-measure, steady-state Frequency Response Functions (FRFs) to develop a state-space dynamical model of the structure under test. The developed model is then used to study the transient response of the structure and estimate its dispersion curves. This paper lays down the foundation of this approach and demonstrates its capabilities on a one-dimensional homogeneous beam using numerically calculated FRFs. Both in-plane and out-of-plane FRFs corresponding, respectively, to longitudinal (the first symmetric) and flexural (the first anti-symmetric) wave modes are analyzed. The effects of boundary conditions on the performance of this approach are also addressed.
机译：由于需要描述和理解结构材料和构件中的波传播，已经开发了几种分析，数值和实验技术来获得色散曲线。分析和数值方法需要对被测结构（波导）进行精确表征。另一方面，实验方法依赖于分析沿结构传播的波形。材料的不均匀性，边界的反射以及被测结构的物理尺寸限制了可以测量色散曲线的频率范围。在这项工作中，开发了一种用于估计色散曲线的新的数据驱动建模方法。这种方法利用相对易于测量的稳态频率响应函数（FRF）来开发被测结构的状态空间动力学模型。然后将开发的模型用于研究结构的瞬态响应并估计其色散曲线。本文奠定了该方法的基础，并演示了使用数值计算的FRF在一维均质梁上的功能。分析分别对应于纵向（第一对称）和弯曲（第一反对称）波模式的平面内和平面外FRF。还讨论了边界条件对该方法性能的影响。

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