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首页> 外文期刊>International Journal of Solids and Structures >Discriminating linear from nonlinear elastic damage using a nonlinear time reversal DORT method
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Discriminating linear from nonlinear elastic damage using a nonlinear time reversal DORT method

机译：使用非线性时间反转DORT方法将线性与非线性弹性损伤区分开

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摘要

The DORT method is a selective detection and focusing technique originally developed to detect defects and damages which induce linear changes of the elastic moduli. It is based on the time reversal (TR) where a signal collected from an array of transducers is time reversed and then back-propagated into the medium to obtain focusing on selected targets. TR is based on the principle of spatial reciprocity. Attenuation, dispersion, multiple scattering, mode conversion, etc. do not break spatial reciprocity. The presence of defects or damage, may cause materials to show nonlinear elastic wave propagation behavior that will break spacial reciprocity. Therefore the DORT method will not allow focusing on nonlinear elastic scatterers. This paper presents a new method for the detection and identification of multiple linear and nonlinear scatterers by combining nonlinear elastic wave spectroscopy, time reversal and DORT method. In the presence of nonlinear hysteretic elastic scatterers, forcing the solid with a harmonic excitation, the time reversal operator can be obtained not only at the fundamental frequency of excitation, but also at the odd harmonics. At the fundamental harmonic, either inhomogeneities and linear damages can be individually selected but only at odd harmonics nonlinear hysteretic elastic damages exist. A procedure was developed where by decomposing the operator at the odd harmonics, it was possible to focus on nonlinear scatterers and to differentiate them from the linear inhomogeneities. A complete mathematical nonlinear DORT formulation for 1 and 2D structures is presented. To model the presence of nonlinear elastic hysteretic scatterers a Preisach-Mayergoyz (PM) material constitutive model was used. Results relative to 1 and 2 dimensional structures are reported showing the capability of the method to focus and discern selectively linear and nonlinear scatterers. Furthermore, an analysis was conducted to study the influence of the number of sources and their location on the imaging process showing that using a higher numbers of sensors does not automatically bring to a minor uncoupled behaviour between the nonlinear targets.
机译：DORT方法是一种选择性检测和聚焦技术，最初是为了检测导致弹性模量线性变化的缺陷和损坏而开发的。它基于时间反转（TR），其中将从换能器阵列收集的信号进行时间反转，然后反向传播到介质中，从而获得对选定目标的关注。 TR基于空间互惠原则。衰减，色散，多重散射，模式转换等不会破坏空间互易性。缺陷或损坏的存在可能会导致材料显示非线性弹性波传播行为，从而破坏空间互易性。因此，DORT方法将不允许集中于非线性弹性散射体。结合非线性弹性波光谱，时间反转和DORT方法，提出了一种检测和识别多个线性和非线性散射体的新方法。在存在非线性滞后弹性散射体的情况下，迫使固体受到谐波激励，不仅可以在激励的基频上获得奇数时间倒数算子，还可以在奇次谐波处获得时间倒数算子。在基波谐波处，可以分别选择不均匀性和线性损伤，但仅在奇数谐波处，存在非线性滞回弹性损伤。开发了一种程序，通过分解奇数次谐波处的算符，可以集中于非线性散射体并将其与线性不均匀性区分开。提出了针对1D和2D结构的完整数学非线性DORT公式。为了对非线性弹性滞后散射体的存在进行建模，使用了Preisach-Mayergoyz（PM）材料本构模型。报告了相对于一维和二维结构的结果，表明该方法具有聚焦和辨别选择性线性和非线性散射体的能力。此外，进行了一项分析以研究源的数量及其位置对成像过程的影响，结果表明，使用更多数量的传感器并不会自动导致非线性目标之间的次要解耦行为。

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