| 局部裂纹损伤简支梁的曲率模态特性 |
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| 引用本文： | 徐平.局部裂纹损伤简支梁的曲率模态特性[J].固体力学学报,2011(Z1). |
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| 作者姓名： | 徐平 |
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| 作者单位： | 郑州大学水利与环境学院; |
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| 基金项目： | 国家自然科学基金(51008286)资助 |
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| 摘 要： | 将裂缝损伤简化成矩形凹槽,采用delta函数表示简支梁的裂纹损伤位置,得到了全梁范围内截面转动惯量和单位长度质量的表达式,建立了局部裂缝损伤简支梁的横向自由振动方程.利用摄动方法给出了裂纹摄动项的一般表达式,根据摄动项和完整梁都同时满足边界条件的特点,将一阶和二阶摄动项都表示成完整梁模态的线性组合,结合delta函数的性质,最终获得了受损简支梁的特征值和模态振型的解析表达式.最后,通过数值计算得到结构模态参数,对比了一阶摄动和二阶摄动对计算结果的影响,分析了不同阶固有频率和模态曲率的变动量,为简支梁的损伤监控和检测提供了理论依据.
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| 关 键 词： | 裂纹损伤 简支梁 摄动方法 模态分析方法 曲率模态 |
MODAL CURVATURE CHARACTERISTICS OF A SIMPLE BEAM WITH A LOCAL DAMAGED CRACK |
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| Ping Xu.MODAL CURVATURE CHARACTERISTICS OF A SIMPLE BEAM WITH A LOCAL DAMAGED CRACK[J].Acta Mechnica Solida Sinica,2011(Z1). |
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| Authors: | Ping Xu |
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| Institution: | Ping Xu(School of Water Conservancy and Environment Engineering,Zhengzhou University,Zhengzhou,450002) |
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| Abstract: | The damaged crack is assumed as a rectangle groove,the crack position at the simple beam is located with delta function,the expressions of cross-section rotary inertia and mass per unit length of the whole beam are founded,and then the transverse free vibration equation of the simple beam with a damaged crack is established.The general expressions of crack perturbations are given with perturbation method,the first and second perturbations are considered as the linear combinations of corresponding mode shape... |
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| Keywords: | crack damage simple beam perturbation method modal analysis curvature mode |
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