Development of non-destructive detection system of breathing cracks using dynamic response

在这个项目中，我们首先发展了一种分析带有呼吸性裂纹的梁的振动的方法。在改进的方法中，控制方程采用基于混合变分原理的有限元方法。然后，用增量谐波平衡法求解控制方程。结果表明，该方法可以较高的精度和效率地分析含呼吸性裂纹梁的稳态振动。接下来，基于所开发的分析方法，我们开发了一种基于动力响应的梁中呼吸裂缝的检测技术。通过数值模拟验证了所提出的检测技术能够准确检测出呼吸性裂纹。接下来，为了进一步检验所开发的检测技术的适用性，我们进行了实验。在实验中，我们使用了一根有呼吸裂纹的钢梁。用薄锯片模拟呼吸裂纹，在锯片上插入厚度与锯片宽度相同的薄钢板。我们用实验测得的数据来检测裂纹。观察了准确的检测结果。从而证实了所开发的束流探测技术的适用性。最后，我们将梁的检测技术扩展到以管道系统为典型的框架结构的检测技术。本文提出的基于混合变分原理的分析方法具有不需作较大修改即可应用于此类框架结构的特点。因此，框架结构的检测技术的过程与梁的检测技术的过程非常相似。通过数值模拟验证了扩展检测技术的适用性。

In this project, first, we developed a method for vibration analysis of a beam with breathing cracks. In the developed method, the governing equations are formulated using the finite element method based on the mixed variational principle. Then, the governing equation is solved using the incremental harmonic balance method. We confirmed that the developed method can analyze steady-state vibrations of a beam with breathing cracks with high accuracy and efficiency. Next, we developed a detection technique of breathing cracks in a beam using dynamic response based on the developed analysis method. We confirmed via numerical simulation that the developed detection technique can detect breathing cracks accurately. Next, in order to check further the applicability of the developed detection technique, we conducted experiment. In the experiment we used a steel beam with a breathing crack. The breathing crack was simulated by a thin saw-cut to which the thin steel plate with the same thickness as the width of the saw-cut was inserted. We used measured data from the experiment to detect the crack. The accurate detection result was observed. Thus we confirmed the applicability of the developed detection technique for a beam. Finally, we extended the detection technique for a beam to a technique for a frame structure whose typical is a piping system. The developed analysis method based on the mixed variational principle has feature that it can be applied to such a frame structure without large modification. Thus the procedure of the detection technique for a frame structure is very similar to that for a beam. The applicability of the extended detection technique was confirmed by numerical simulation.