裂纹损伤结构的振动功率流特性与损伤识别
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摘要
本文的研究工作是国家自然科学基金项目“基于振动能量流分析的损伤结构波动特性与损伤识别(50375059)”的一部分。本文对裂纹损伤结构的振动功率流特性进行了理论研究和实验研究,并在此基础上提出了基于结构功率流的裂纹识别方法。在理论上将振动功率流的研究发展到结构损伤识别领域,在应用上提出新的识别结构损伤的测量和分析方法。
文中首先对梁结构和板壳结构中比较常见的裂纹进行了模拟研究。根据断裂力学相关理论推导了一维裂纹损伤结构在耦合外载荷作用下在裂纹区域的局部柔度矩阵,并详细推导了弯曲载荷作用下圆形截面和矩形截面裂纹梁的局部柔度并对局部柔度曲线进行了拟合。利用线弹簧模型来模拟板壳结构中的表面裂纹和内部裂纹,将三维裂纹模型简化为裂纹线上作用有分布线弹簧的二维穿透裂纹模型,推导出了线弹簧模型的局部柔度计算公式。
接着分别对含有裂纹的Timoshenko梁结构和薄板结构的振动功率流特性进行了研究。对于梁结构,将裂纹模拟为转动弹簧,对于板结构,则将裂纹模拟为线弹簧。对裂纹梁和板结构的波动特性进行了理论分析,在此基础上对裂纹结构功率流输入和传播特性进行了计算;讨论了裂纹的位置、深度等参数与输入以及传播功率流之间的联系。构造不同裂纹位置和裂纹深度的组合下的归一化输入功率流等值线图。首次提出了利用不同激励频率下裂纹损伤结构的输入能量流等值线图识别结构的裂纹位置和裂纹深度的方法,利用该方法可以对裂纹进行有效的识别。对该方法在含噪声条件下的灵敏度进行了分析,表明此方法对噪声不太敏感。
对工程中广泛使用的圆柱壳结构进行了研究,首次分析了含环向裂纹损伤的圆柱薄壳的振动功率流特性。利用线弹簧模型模拟裂纹,对裂纹的张开、滑移和剪切三种状态建立了裂纹区域的局部柔度矩阵,壳体的振动用Flügge方程来描述,考虑壳体中各种不同类型的波,利用波型叠加法得到了外激励力作用下输入到壳体中的输入能量以及能量的传播,讨论了功率流特性与裂纹位置和尺寸以及壳体特性等参数的关系。给出了利用归一化输入功率流对壳体裂纹进行识别的方法。
利用有限单元法对裂纹损伤结构的功率流进行了可视化研究。首先引入了结构声强的概念,给出了有限元一维、二维和三维单元中结构声强的表达式。然后给出了流线可视化的概念,并应用到结构声强流线的可视化中。针对含有裂纹的弹性体,推导出了结构在动载荷作用下的结构声强和J积分之间的关系。计算得到了裂纹结构在不同裂纹参数和不同激励频率下的位移响应矢量图、声强矢量图和流线图。实现了对结构表面能量分布、传播以及在裂纹位置周围的分布规律的可视化,为掌握振动能量在损伤结构的传播、损伤的识别提供了新的手段。
文章的最后对含有环向表面裂纹损伤的圆柱壳结构的振动功率流进行了试验研究。基于传感器技术提出了对裂纹圆柱壳输入功率流进行测量并进行裂纹识别的方法和程序。试验结果与理论计算结果基本吻合,表明本文的理论推导和计算方法正确,模型设计合理。最后对试验进行了误差分析。
The work of this thesis is a part of the research project”the wave characteristics of damaged structures based on vibrational power flow and the damage detection”. In this thesis, the vibrational power flow characteristics of cracked structures are researched theoretically and experimentally, and the crack detection method based on the vibrational power flow are proposed. The research enlarges the research scope of the vibration energy flow into the field of damage detection theoretically and proposes a new method to damage detection in engineering.
Firstly, the modeling of cracks in the beam, plate and shell structures which often occur in engineering are investigated. Based on the fracture mechanics, the local flexibility matrix of the one-dimensional cracked structures under the coupled loads is deduced. Then the local flexibilities in a circular-section and solid rectangular-sectional beam under the bending moment are addressed respectively, by applying the least-squares method the best-fitted explicit expression of the local flexibility versus crack depth is given. The surface cracks and inner cracks in the plate and shell structures are modeled by line spring. By the transformation of three-dimensional crack issue into two-dimensional model, the local compliance of the line spring is obtained.
Then the power flow characteristics of cracked Timoshenko beams and cracked thin plates are researched. The existence of the crack in the cracked structures induces the local compliance, which in turn changes the dynamic response of the cracked structures. The crack is modeled as a rational spring for beam structures and line spring for plate structures. The input power flow and transmitted power flow in cracked structures are calculated, then the relationship between the power flow characteristics and the crack information (location and depth) are discussed. The contour lines diagram of input power flow with two different driving frequencies is constructed to identify the crack, which can successfully indicate the crack’s information. The sensitivity of the method is discussed.
For the circular cylindrical shell structure widely used in the engineering, the vibrational power flow characteristics of thin shell with circumferential crack are investigated for the first time. The equivalent distributed line spring is designed to model the surface or inner crack in the shell. The local compliance matrix due to the presence of the crack is deduced from fracture mechanics and three modes of the crack stress intensity factors and their coupling are considered in the local compliance matrix. The vibration of the shell is descirbed by Flugge’s shell equations. Under the excitation of radial harmonic line force, the input power flow and transmitted power flow of uncracked and cracked shells are obtained. The results show that the vibrational power flow of cracked shell changes substantially due to the presence of crack, and the change is strongly related to the depth and location of crack. Contours of input power flow under different frequencies are constructed to identify the location and depth of the crack.
The visualization of power flow in the cracked structures are studied based on finite element method(FEM) for the first time. By introducing the concept of structural intensity(SI), the detail expressions of SI in one-dimensional, two-dimensional and three-dimensional structures are given. The streamline techque is empolyed in the visualization of SI vector field. For the elastic solid with crack, the relationship between the J integal and SI is deduced. The displacement vector plot, SI vector plot and streamline plot are obtained for different crack parameters and different dirving frequencies. The distrubition and propagation of surface energy flow in cracked structure and near the crack are given, which provides a new tool for crack detection.
At last, the experimental research on the cracked cylindrical shell’s input power flow is implemented. Based on sensor technology, the input power flow of cracked shell are measured. The experimental results and theoretical results show a agreement in substance, which demonstrate the accuracy of the theory and the reasonability of the experimental model’s setup. The errors in the experiment are analyzed as well.
文中首先对梁结构和板壳结构中比较常见的裂纹进行了模拟研究。根据断裂力学相关理论推导了一维裂纹损伤结构在耦合外载荷作用下在裂纹区域的局部柔度矩阵,并详细推导了弯曲载荷作用下圆形截面和矩形截面裂纹梁的局部柔度并对局部柔度曲线进行了拟合。利用线弹簧模型来模拟板壳结构中的表面裂纹和内部裂纹,将三维裂纹模型简化为裂纹线上作用有分布线弹簧的二维穿透裂纹模型,推导出了线弹簧模型的局部柔度计算公式。
接着分别对含有裂纹的Timoshenko梁结构和薄板结构的振动功率流特性进行了研究。对于梁结构,将裂纹模拟为转动弹簧,对于板结构,则将裂纹模拟为线弹簧。对裂纹梁和板结构的波动特性进行了理论分析,在此基础上对裂纹结构功率流输入和传播特性进行了计算;讨论了裂纹的位置、深度等参数与输入以及传播功率流之间的联系。构造不同裂纹位置和裂纹深度的组合下的归一化输入功率流等值线图。首次提出了利用不同激励频率下裂纹损伤结构的输入能量流等值线图识别结构的裂纹位置和裂纹深度的方法,利用该方法可以对裂纹进行有效的识别。对该方法在含噪声条件下的灵敏度进行了分析,表明此方法对噪声不太敏感。
对工程中广泛使用的圆柱壳结构进行了研究,首次分析了含环向裂纹损伤的圆柱薄壳的振动功率流特性。利用线弹簧模型模拟裂纹,对裂纹的张开、滑移和剪切三种状态建立了裂纹区域的局部柔度矩阵,壳体的振动用Flügge方程来描述,考虑壳体中各种不同类型的波,利用波型叠加法得到了外激励力作用下输入到壳体中的输入能量以及能量的传播,讨论了功率流特性与裂纹位置和尺寸以及壳体特性等参数的关系。给出了利用归一化输入功率流对壳体裂纹进行识别的方法。
利用有限单元法对裂纹损伤结构的功率流进行了可视化研究。首先引入了结构声强的概念,给出了有限元一维、二维和三维单元中结构声强的表达式。然后给出了流线可视化的概念,并应用到结构声强流线的可视化中。针对含有裂纹的弹性体,推导出了结构在动载荷作用下的结构声强和J积分之间的关系。计算得到了裂纹结构在不同裂纹参数和不同激励频率下的位移响应矢量图、声强矢量图和流线图。实现了对结构表面能量分布、传播以及在裂纹位置周围的分布规律的可视化,为掌握振动能量在损伤结构的传播、损伤的识别提供了新的手段。
文章的最后对含有环向表面裂纹损伤的圆柱壳结构的振动功率流进行了试验研究。基于传感器技术提出了对裂纹圆柱壳输入功率流进行测量并进行裂纹识别的方法和程序。试验结果与理论计算结果基本吻合,表明本文的理论推导和计算方法正确,模型设计合理。最后对试验进行了误差分析。
The work of this thesis is a part of the research project”the wave characteristics of damaged structures based on vibrational power flow and the damage detection”. In this thesis, the vibrational power flow characteristics of cracked structures are researched theoretically and experimentally, and the crack detection method based on the vibrational power flow are proposed. The research enlarges the research scope of the vibration energy flow into the field of damage detection theoretically and proposes a new method to damage detection in engineering.
Firstly, the modeling of cracks in the beam, plate and shell structures which often occur in engineering are investigated. Based on the fracture mechanics, the local flexibility matrix of the one-dimensional cracked structures under the coupled loads is deduced. Then the local flexibilities in a circular-section and solid rectangular-sectional beam under the bending moment are addressed respectively, by applying the least-squares method the best-fitted explicit expression of the local flexibility versus crack depth is given. The surface cracks and inner cracks in the plate and shell structures are modeled by line spring. By the transformation of three-dimensional crack issue into two-dimensional model, the local compliance of the line spring is obtained.
Then the power flow characteristics of cracked Timoshenko beams and cracked thin plates are researched. The existence of the crack in the cracked structures induces the local compliance, which in turn changes the dynamic response of the cracked structures. The crack is modeled as a rational spring for beam structures and line spring for plate structures. The input power flow and transmitted power flow in cracked structures are calculated, then the relationship between the power flow characteristics and the crack information (location and depth) are discussed. The contour lines diagram of input power flow with two different driving frequencies is constructed to identify the crack, which can successfully indicate the crack’s information. The sensitivity of the method is discussed.
For the circular cylindrical shell structure widely used in the engineering, the vibrational power flow characteristics of thin shell with circumferential crack are investigated for the first time. The equivalent distributed line spring is designed to model the surface or inner crack in the shell. The local compliance matrix due to the presence of the crack is deduced from fracture mechanics and three modes of the crack stress intensity factors and their coupling are considered in the local compliance matrix. The vibration of the shell is descirbed by Flugge’s shell equations. Under the excitation of radial harmonic line force, the input power flow and transmitted power flow of uncracked and cracked shells are obtained. The results show that the vibrational power flow of cracked shell changes substantially due to the presence of crack, and the change is strongly related to the depth and location of crack. Contours of input power flow under different frequencies are constructed to identify the location and depth of the crack.
The visualization of power flow in the cracked structures are studied based on finite element method(FEM) for the first time. By introducing the concept of structural intensity(SI), the detail expressions of SI in one-dimensional, two-dimensional and three-dimensional structures are given. The streamline techque is empolyed in the visualization of SI vector field. For the elastic solid with crack, the relationship between the J integal and SI is deduced. The displacement vector plot, SI vector plot and streamline plot are obtained for different crack parameters and different dirving frequencies. The distrubition and propagation of surface energy flow in cracked structure and near the crack are given, which provides a new tool for crack detection.
At last, the experimental research on the cracked cylindrical shell’s input power flow is implemented. Based on sensor technology, the input power flow of cracked shell are measured. The experimental results and theoretical results show a agreement in substance, which demonstrate the accuracy of the theory and the reasonability of the experimental model’s setup. The errors in the experiment are analyzed as well.
引文
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