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含裂纹圆截面梁损伤识别频率等高线法
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国家自然科学基金地区科学基金项目(51965042);江西省自然科学基金面上项目(20181BAB206023);南昌航空大学研究生创新资金(YC2018014)


Damage Identification of Cracked Circular Cross Section Beam by Frequency Contour Line Method
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    摘要:

    圆形截面梁广泛应用于机械设备与道路桥梁等领域中,裂纹的存在及扩展直接危及梁的安全可靠性,进而引发灾难性事故。旨在研究一种基于频率等高线的裂纹识别方法。使用一种新方法推导了裂纹梁在轴力、剪力和弯矩共同作用时的应力强度因子,给出了相应的柔度系数计算公式。基于有限元法分别推导了含裂纹单元和无裂纹单元的柔度矩阵,推导了梁的振动方程,探讨了裂纹对梁模态频率的影响。在此基础上,将固有频率作为裂纹识别的判断指针,研究了圆形截面梁裂纹识别频率等高线法。最后,基于频率误差函数对固有频率等高线法进行改良,提高了裂纹识别精度。结果表明:改良后的频率等高线法弥补了其在一些工况下无交点甚至无三角形区域的缺陷,使它更具工程应用可行性,并且该方法对裂纹位置和深度的识别也较为精准,相对裂纹深度识别最大误差为77.5%,相对裂纹位置识别最大误差仅为12.6%。

    Abstract:

    The circular cross section beam is widely used in mechanical equipment and civil engineering. The existence of cracks directly endangers safety and reliability of beam. A crack identification method based on frequency contour line was explored.The evaluations of stress intensity factors for a beam subjected to tension, bending moment and shear were deduced by using a new method, and the evaluations of corresponding flexibility coefficient were given. According to FEM, the compliance matrices of cracked and uncracked element beam were derived, the motion differential equation for free vibration was given, and the vibration characteristic of the beam with crack was discussed. By means of the influence of the crack parameters on the natural frequency, the natural frequency was used as a detector, and the crack was identified by the natural frequency contour line method, the method was improved based on experiments. The results show that the improved frequency contour method makes up for the deficiency that there is no intersection or triangle in some conditions, making it more feasible in engineering practice, and the maximum error of the relative crack depth is 77.5%, the maximum error of the relative crack location is only 12.6%.

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戴文柯,刘文光.含裂纹圆截面梁损伤识别频率等高线法[J].机床与液压,2021,49(7):26-32.
DAI Wenke, LIU Wenguang. Damage Identification of Cracked Circular Cross Section Beam by Frequency Contour Line Method[J]. Machine Tool & Hydraulics,2021,49(7):26-32

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  • 在线发布日期: 2023-03-01
  • 出版日期: 2021-04-15