基于柔度曲率矩阵的结构损伤识别研究
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摘要
结构损伤识别的主要研究内容是对各种工程结构进行检测并对检测结果做适当的分析,从而确定该结构的健康状况。它所处理的是结构内部、肉眼不可见的损伤,检测手段通常要求是非破坏性的,而识别结果将作为结构安全使用与维护的重要依据。各种识别方法要解决的三个关键问题是:(1)结构中是否存在损伤;(2)确定结构中损伤的位置;(3)确定损伤的程度或形式。损伤识别问题的提出有着重要的工程背景,其研究涉及航空航天、交通运输及建筑等众多领域。同时结构损伤识别也是力学和工程中一类典型的反问题,其中工程实际中提出的反问题往往是待定多个未知函数,即几类反问题可能在一个实际问题中同时出现。为了简化求解或使求解成为可能,常用的处理方法是把某些待定或不确定的函数视为已知,先分解难点,再逐步进行求解,所以损伤识别也同时具有理论意义。
结构损伤会对结构的物理特性如刚度、质量、阻尼等产生影响,那么结构的模态参数如固有频率、振型等也会随之改变,这些现象被广泛的应用到结构损伤监控和检测中,所以将结构振动测试数据用于结构损伤识别的研究得到了众多研究者的重视。研究表明模态柔度比固有频率或振型对局部损伤更敏感,可以很好地用于识别结构损伤。
柔度矩阵可通过由测试得到的结构前几阶固有频率和模态振型来较为精确地构造出来。根据振动理论,对于多自由度系统,利用柔度矩阵与刚度矩阵的互逆性,可得到柔度矩阵。柔度矩阵元素反比于固有频率的平方,即低阶振动的模态和频率信息在柔度矩阵中所占的影响成分很大。实际应用中一般只能测得结构最低的几阶模态与频率,以此来近似得出实际的柔度矩阵。在利用结构刚度矩阵进行损伤识别的算法中,有限的低阶模态信息使刚度矩阵的近似误差较大,而利用柔度矩阵则可避免这一缺点。
提出了基于柔度曲率的板结构损伤识别的理论,推导了二维结构的柔度曲率公式并基于此公式给出板结构的损伤指标即柔度曲率矩阵。此理论在判断板结构中是否存在损伤的同时即可判断结构中损伤的位置。之后定义了等效柔度曲率变化率,给出了ECR-SD曲线并通过仿真模拟,回归了板结构的损伤程度的判别公式。仿真分析表明,该方法可以很好的判断损伤位置及损伤程度。
基于板结构理论发展了基于柔度曲率的加筋板结构损伤识别的理论,先对加筋板中板结构进行识别,然后对筋进行损伤识别。由损伤结构的柔度曲率矩阵绘出图像,或者由矩阵的行或列曲率图,通过比较就能直接得出损伤位置。通过数值仿真给出了另外几个不同于原来的重要的损伤指标矩阵,验证并完善了所提出的理论。通过这些损伤指标矩阵可以将加筋板结构的多损伤识别过程简化为至多两个损伤的损伤识别。
建立了基于柔度曲率的柱壳结构损伤识别的理论。提出一种基于柔度曲率的柱壳结构的分析方法和判断准则,首先得到柔度损伤指标矩阵,再对柱壳结构的轴向、周向分别进行柔度曲率分析来判断损伤位置。其中在轴向分析中通过类似于第二章的分析方法得到轴向柔度曲率矩阵;在周向分析中把管状结构考虑成为一组“圆环结构”的集合,再借鉴圆曲率的方法,得到了周向的柔度曲率矩阵,通过轴向或周向的柔度曲率矩阵,就可以对损伤位置进行较好的判断。在仿真分析中可以看出,无论位移还是转角的柔度曲率矩阵能够很好的判断损伤位置。定义了柔度曲率变化率,给出了ECR-SD曲线,并通过大量的仿真分析回归了损伤程度公式。在损伤定位的同时,通过损伤位置的坐标以及柔度曲率变化率就可以进行损伤程度的分析。
进行了对边简支和三边简支的损伤铝板的模态实验,得到了两种板结构的模态振型和固有频率。其中对边简支板结构进行了SISO模态实验与纯模态实验,三边简支进行了SISO模态实验。通过所得到的数据进行板结构的损伤识别,进而来验证本文前面所提出的理论方法,实验结果虽然不像仿真模拟中的效果明显,但还是可以较好进行损伤识别,其中用纯模态实验中得到的模态数据进行损伤识别结果较好。
用结构模态对结构进行损伤识别,通常都要用到结构未损伤前的模态信息。对于机械工程、船舶工程、海洋平台等大型工程结构,就要在工程结构建好之后,马上进行模态分析,以备份未损伤的模态信息,但这就需要大量的人力物力,这是不经济的,因此,没有原始模态参数的结构损伤技术就显得格外重要。以上方法都是基于柔度曲率而建立起来的,它们不需要结构原始的模态参数,即未损伤结构的数据,而且仅需要低阶模态信息即可进行损伤识别。它们都具有以下两个优点:(1)计算量小、简便易行;(2)模态柔度既可以从静力学方法获得,也可以通过动力学的方法获得,或者综合两种方法得到。
The main research contents of structural damage identification are to determine the structure of health status through tested various engineering structures and appropriately analysis these tested results. It deals with the damage which is in the internal structure or invisible with the naked eye. Detection methods often require non-destructive and recognition results will be an important basis as safe use and maintenance of the structure. There are three key questions to solute in various identification methods: 1) whether the damage is existence in the structure; 2) to determine the damage location of the structure; 3) to confirm the damage degree or damage form. Damage identification has important engineering background, the research concern aerospace, transportation, architecture, and many other fields. It is also a class of typical inverse problem in mechanics and engineering, the inverse problem in engineering is to be determined the anti-multiple unknown functions, namely, the anti-types inverse problem may appear at the same time in one practical problem. In order to simplify the solving or make it possible to solve, regard being determined or considered functions as known in commonly used methods, first decomposition of the difficulties, and then gradually solved. So damage identification also has theoretical significance.
Damage generally produces changes in the structural physical properties (i.e., stiffness, mass, and damping), and these changes are accompanied by changes in the modal characteristics of the structure (i.e., natural frequencies, mode shapes, and modal damping). This phenomenon has been widely noted and used by structural engineers for detecting damage or health monitoring of a structure. Therefore, the study of structural vibration test data for structural damage identification has received much attention by many researchers. Some researchers used modal flexibility changes to identify structural damage, discovered and pointed out that the modal flexibility is more sensitive to local damage than the natural frequency or mode shape and thought that it can be well used to identify structural damage.
Flexibility matrix can be more accurately obtained by the first few natural frequencies and modal shape through the tested data from the structure. According to vibration theory, for many degrees of freedom systems, the flexibility matrix is obtained by reciprocal relations between flexibility matrix and stiffness matrix. Flexibility matrix elements inverse ratio square of the natural frequencies, that is, low-vibration mode and frequency in the flexibility matrix has a great impact. The lowest few modes and frequency can only be measured in practical applications and the flexibility matrix can be approximately obtained through these tested data. In the algorithm for damage identification using of the structure stiffness matrix, the approximate error is large with modal stiffness matrix which is obtained by limited low-level modal information, but flexibility matrix can be avoided this shortcoming.
Proposed plate structural damage identification theory based on flexibility curvature. Derived flexibility curvature formula of two-dimensional structure, and the damage index of plate based on these formula, namely flexibility curvature matrix. The theory can determine whether the damage is existence in plate structure and confirm the damage location at the same time. Equivalent curvature ratio is defined and regression the discriminating formula about degree of damage through simulation. Simulation analysis showed that the method can well determine the damage location and degree of damage.
Through the plate structure theory developed the stiffened panel structural damage identification theory based on flexibility curvature. Firstly, plate of stiffened panel is identified. Secondly, the tendon of stiffened panel is identified. The damage location can be determined by the figures of flexibility curvature matrix about damaged structure or by the rows or columns of flexibility curvature matrix. A few important matrices as damage indices are given through simulation experiments. Verified and optimized the theory by these index matrices. The damage identification process of the stiffened panel structure is given at the same time.
The cylindrical structure damage identification theory based on the flexibility curvature is set up. The tubular structure analysis method and judging criteria which is based on the flexibility curvature is proposed. Firstly, the damage index of flexibility matrix is obtained, and then analysis the axial and circumferential flexibility curvature. Consider structure using the theory of chapter two in axial direction to obtain the flexibility curvature matrix. Circumferential flexibility curvature matrix can be obtained by circular curvature. The damage can be well determined through the axial or circumferential flexibility curvature matrix. The flexibility curvature matrix about both displacement and rotation can detect the damage well in the simulation analysis. Equivalent curvature ratio is defined, the curve of ECR-SD is given and regression the discriminating formula about degree of damage through much simulation. The location of damage can be analysis by index matrix and the degree of damage can be analysis by the damage coordinates and equivalent curvature ratio.
Modal experiment of simply supported plate with opposite edges and simply supported plate with three edges is carried out. The mode and natural frequency of these two plates are obtained. SISO modal experiment and pure modal experiment are carried out with simply supported plate with three edges. SISO modal experiment is carried out with simply supported plate with three edges. The theory which is proposed is verified through the damage identification by the data from the experiments. The results of experiment are not better than the simulation experiments, but they can also detect the damage. The results of pure modal experiment are better than others.
Damage identification usually used the modal information from the structure before damage. For mechanical engineering, marine engineering, marine platforms and other large engineering structures, it is not economic to backup mode information after completion, because these need many resources. So the technology is more important with no original modal parameters to identify damage. The above methods are built up based on curvature of flexibility, they do not need original structure data and only need low modal information to make damage detection. All of them have two advantages: 1) less calculation amount and simple execution; 2) Modal flexibility can be obtained from static or dynamic method, or be integrated in two ways.
结构损伤会对结构的物理特性如刚度、质量、阻尼等产生影响,那么结构的模态参数如固有频率、振型等也会随之改变,这些现象被广泛的应用到结构损伤监控和检测中,所以将结构振动测试数据用于结构损伤识别的研究得到了众多研究者的重视。研究表明模态柔度比固有频率或振型对局部损伤更敏感,可以很好地用于识别结构损伤。
柔度矩阵可通过由测试得到的结构前几阶固有频率和模态振型来较为精确地构造出来。根据振动理论,对于多自由度系统,利用柔度矩阵与刚度矩阵的互逆性,可得到柔度矩阵。柔度矩阵元素反比于固有频率的平方,即低阶振动的模态和频率信息在柔度矩阵中所占的影响成分很大。实际应用中一般只能测得结构最低的几阶模态与频率,以此来近似得出实际的柔度矩阵。在利用结构刚度矩阵进行损伤识别的算法中,有限的低阶模态信息使刚度矩阵的近似误差较大,而利用柔度矩阵则可避免这一缺点。
提出了基于柔度曲率的板结构损伤识别的理论,推导了二维结构的柔度曲率公式并基于此公式给出板结构的损伤指标即柔度曲率矩阵。此理论在判断板结构中是否存在损伤的同时即可判断结构中损伤的位置。之后定义了等效柔度曲率变化率,给出了ECR-SD曲线并通过仿真模拟,回归了板结构的损伤程度的判别公式。仿真分析表明,该方法可以很好的判断损伤位置及损伤程度。
基于板结构理论发展了基于柔度曲率的加筋板结构损伤识别的理论,先对加筋板中板结构进行识别,然后对筋进行损伤识别。由损伤结构的柔度曲率矩阵绘出图像,或者由矩阵的行或列曲率图,通过比较就能直接得出损伤位置。通过数值仿真给出了另外几个不同于原来的重要的损伤指标矩阵,验证并完善了所提出的理论。通过这些损伤指标矩阵可以将加筋板结构的多损伤识别过程简化为至多两个损伤的损伤识别。
建立了基于柔度曲率的柱壳结构损伤识别的理论。提出一种基于柔度曲率的柱壳结构的分析方法和判断准则,首先得到柔度损伤指标矩阵,再对柱壳结构的轴向、周向分别进行柔度曲率分析来判断损伤位置。其中在轴向分析中通过类似于第二章的分析方法得到轴向柔度曲率矩阵;在周向分析中把管状结构考虑成为一组“圆环结构”的集合,再借鉴圆曲率的方法,得到了周向的柔度曲率矩阵,通过轴向或周向的柔度曲率矩阵,就可以对损伤位置进行较好的判断。在仿真分析中可以看出,无论位移还是转角的柔度曲率矩阵能够很好的判断损伤位置。定义了柔度曲率变化率,给出了ECR-SD曲线,并通过大量的仿真分析回归了损伤程度公式。在损伤定位的同时,通过损伤位置的坐标以及柔度曲率变化率就可以进行损伤程度的分析。
进行了对边简支和三边简支的损伤铝板的模态实验,得到了两种板结构的模态振型和固有频率。其中对边简支板结构进行了SISO模态实验与纯模态实验,三边简支进行了SISO模态实验。通过所得到的数据进行板结构的损伤识别,进而来验证本文前面所提出的理论方法,实验结果虽然不像仿真模拟中的效果明显,但还是可以较好进行损伤识别,其中用纯模态实验中得到的模态数据进行损伤识别结果较好。
用结构模态对结构进行损伤识别,通常都要用到结构未损伤前的模态信息。对于机械工程、船舶工程、海洋平台等大型工程结构,就要在工程结构建好之后,马上进行模态分析,以备份未损伤的模态信息,但这就需要大量的人力物力,这是不经济的,因此,没有原始模态参数的结构损伤技术就显得格外重要。以上方法都是基于柔度曲率而建立起来的,它们不需要结构原始的模态参数,即未损伤结构的数据,而且仅需要低阶模态信息即可进行损伤识别。它们都具有以下两个优点:(1)计算量小、简便易行;(2)模态柔度既可以从静力学方法获得,也可以通过动力学的方法获得,或者综合两种方法得到。
The main research contents of structural damage identification are to determine the structure of health status through tested various engineering structures and appropriately analysis these tested results. It deals with the damage which is in the internal structure or invisible with the naked eye. Detection methods often require non-destructive and recognition results will be an important basis as safe use and maintenance of the structure. There are three key questions to solute in various identification methods: 1) whether the damage is existence in the structure; 2) to determine the damage location of the structure; 3) to confirm the damage degree or damage form. Damage identification has important engineering background, the research concern aerospace, transportation, architecture, and many other fields. It is also a class of typical inverse problem in mechanics and engineering, the inverse problem in engineering is to be determined the anti-multiple unknown functions, namely, the anti-types inverse problem may appear at the same time in one practical problem. In order to simplify the solving or make it possible to solve, regard being determined or considered functions as known in commonly used methods, first decomposition of the difficulties, and then gradually solved. So damage identification also has theoretical significance.
Damage generally produces changes in the structural physical properties (i.e., stiffness, mass, and damping), and these changes are accompanied by changes in the modal characteristics of the structure (i.e., natural frequencies, mode shapes, and modal damping). This phenomenon has been widely noted and used by structural engineers for detecting damage or health monitoring of a structure. Therefore, the study of structural vibration test data for structural damage identification has received much attention by many researchers. Some researchers used modal flexibility changes to identify structural damage, discovered and pointed out that the modal flexibility is more sensitive to local damage than the natural frequency or mode shape and thought that it can be well used to identify structural damage.
Flexibility matrix can be more accurately obtained by the first few natural frequencies and modal shape through the tested data from the structure. According to vibration theory, for many degrees of freedom systems, the flexibility matrix is obtained by reciprocal relations between flexibility matrix and stiffness matrix. Flexibility matrix elements inverse ratio square of the natural frequencies, that is, low-vibration mode and frequency in the flexibility matrix has a great impact. The lowest few modes and frequency can only be measured in practical applications and the flexibility matrix can be approximately obtained through these tested data. In the algorithm for damage identification using of the structure stiffness matrix, the approximate error is large with modal stiffness matrix which is obtained by limited low-level modal information, but flexibility matrix can be avoided this shortcoming.
Proposed plate structural damage identification theory based on flexibility curvature. Derived flexibility curvature formula of two-dimensional structure, and the damage index of plate based on these formula, namely flexibility curvature matrix. The theory can determine whether the damage is existence in plate structure and confirm the damage location at the same time. Equivalent curvature ratio is defined and regression the discriminating formula about degree of damage through simulation. Simulation analysis showed that the method can well determine the damage location and degree of damage.
Through the plate structure theory developed the stiffened panel structural damage identification theory based on flexibility curvature. Firstly, plate of stiffened panel is identified. Secondly, the tendon of stiffened panel is identified. The damage location can be determined by the figures of flexibility curvature matrix about damaged structure or by the rows or columns of flexibility curvature matrix. A few important matrices as damage indices are given through simulation experiments. Verified and optimized the theory by these index matrices. The damage identification process of the stiffened panel structure is given at the same time.
The cylindrical structure damage identification theory based on the flexibility curvature is set up. The tubular structure analysis method and judging criteria which is based on the flexibility curvature is proposed. Firstly, the damage index of flexibility matrix is obtained, and then analysis the axial and circumferential flexibility curvature. Consider structure using the theory of chapter two in axial direction to obtain the flexibility curvature matrix. Circumferential flexibility curvature matrix can be obtained by circular curvature. The damage can be well determined through the axial or circumferential flexibility curvature matrix. The flexibility curvature matrix about both displacement and rotation can detect the damage well in the simulation analysis. Equivalent curvature ratio is defined, the curve of ECR-SD is given and regression the discriminating formula about degree of damage through much simulation. The location of damage can be analysis by index matrix and the degree of damage can be analysis by the damage coordinates and equivalent curvature ratio.
Modal experiment of simply supported plate with opposite edges and simply supported plate with three edges is carried out. The mode and natural frequency of these two plates are obtained. SISO modal experiment and pure modal experiment are carried out with simply supported plate with three edges. SISO modal experiment is carried out with simply supported plate with three edges. The theory which is proposed is verified through the damage identification by the data from the experiments. The results of experiment are not better than the simulation experiments, but they can also detect the damage. The results of pure modal experiment are better than others.
Damage identification usually used the modal information from the structure before damage. For mechanical engineering, marine engineering, marine platforms and other large engineering structures, it is not economic to backup mode information after completion, because these need many resources. So the technology is more important with no original modal parameters to identify damage. The above methods are built up based on curvature of flexibility, they do not need original structure data and only need low modal information to make damage detection. All of them have two advantages: 1) less calculation amount and simple execution; 2) Modal flexibility can be obtained from static or dynamic method, or be integrated in two ways.
引文
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