含裂纹圆拱的模态参数分析

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振动与冲击 ›› 2023, Vol. 42 ›› Issue (23) : 199-208.

论文

含裂纹圆拱的模态参数分析

熊峻巍1,2，卢文波1,2，王高辉1,2，刘义佳1,2，王洋1,2

作者信息 +

Modal parametric analysis of circular arch with cracks

XIONG Junwei1,2,LU Wenbo1,2,WANG Gaohui1,2,LIU Yijia1,2,WANG Yang1,2

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文章历史 +

摘要

基于圆拱振动微分方程，引入基于断裂力学的线弹簧模型，分析了含单裂纹圆拱的面内自由振动特性；基于摄动理论，揭示了不同裂纹位置和裂纹深度下结构的模态变化规律；同时结合有限元模型，对比了拱结构内、外侧裂纹对结构模态参数的不同影响。最后，利用损伤拱试验数据，检验了建立的含裂纹拱力学计算模型的适用性与可靠性。结果表明：在拱结构中，各阶模态对裂纹损伤的依赖性不同，当损伤靠近某阶振型峰值点或固定端时，该阶模态固有频率下降显著；同阶模态中拱外侧裂纹在振型峰值较大处对损伤敏感，而内侧裂纹在振型峰值较小处敏感。

Abstract

Based on the oscillatory differential equation of circular arches and the line-spring model from fracture mechanics, the in-plane free vibration characteristics of circular arches with single crack was studied. Based on the perturbation theory, modal variation laws of circular arches under different crack depth and crack position was analyzed. Then, the influence of inner cracks and outer cracks on structural modal parameters was discussed through FEM. Finally, the serviceability and reliability of the mechanical model of cracked arches proposed in this article were examined by comparing with the test data. It is revealed that the dependency of each order modal on crack damage is different. If the damage is close to the peak point of vibration mode or the fixed end of a certain order, the natural frequency of corresponding order decreases significantly. Besides, the outer crack is sensitive to damage near the relatively large peak while the inner crack is more sensitive near the relatively small peak.

导出引用

熊峻巍1,2，卢文波1,2，王高辉1,2，刘义佳1,2，王洋1,2. 含裂纹圆拱的模态参数分析[J]. 振动与冲击, 2023, 42(23): 199-208

XIONG Junwei1,2,LU Wenbo1,2,WANG Gaohui1,2,LIU Yijia1,2,WANG Yang1,2. Modal parametric analysis of circular arch with cracks[J]. Journal of Vibration and Shock, 2023, 42(23): 199-208

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