The local flexibility coefficient equations of a pipe with a circumferential part-through crack subjected to axial force, shearing force and bending moment were derived by using theories of linear fracture mechanics and strain energy release principle.An adaptive Simpson quadrature method was used to conduct numerical integrations to obtain the flexibility coefficients.A finite element model was established to conduct the vibration analysis of a cracked cantilever pipe.In addition, the crack identifiation for the cracked cantilever pipe was investigated based on contour plots of frequency ratio as a function of crack location and crack depth.The results showed that the proposed model overcomes the shortcoming that the existing crack models are suitable only for calculating special loads or structures with non-hollow cross-section, and the contour diagram can identify crack location and depth effectively.%根据线性断裂力学理论和应变能释放原理,推导了含圆周非贯穿裂纹管道在轴力、剪力和弯矩等荷载作用下的局部柔度系数方程,利用适应性Simpson方法编写了数值积分程序进行局部柔度系数求解,建立了含裂纹管道的二维有限元模型进行含裂纹悬臂管道的振动特性分析,应用等值线图原理进行了悬臂管道的裂纹识别.研究结果表明:裂纹模型克服了当前裂纹模型仅针对特定的荷载模式或非空心截面的缺陷,基于等值线图法能有效识别含裂纹悬臂管道的裂纹位置、深度.
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