基于模态应变能变化率法功能梯度Timoshenko梁结构损伤识别的研究

发布时间：2018-05-26 20:57

本文选题：功能梯度材料 + Timoshenko梁　；参考：《广西大学》2016年硕士论文

【摘要】：功能梯度材料(FGMs)是一种材料的性质和功能沿空间方向呈梯度连续变化的新型非均质复合材料,该种材料内部不存在明显的界面,功能梯度材料的这些独特优点使其在航空航天、土木工程、机械工程、化学工程等许多领域得到广泛的应用。由于各种因素导致结构发生损伤,甚至因丧失稳定性而发生灾难,危及人生安全或损失大量财产,所以对功能梯度材料结构进行损伤识别至关重要。基于功能梯度Euler-Bernoulli梁理论,首先推导了2节点6自由度梁单元的模态应变能表达式,然后采用模态应变能变化率法进行Euler-Bernoulli梁结构的损伤识别。在损伤识别过程中,有限元计算得到的模态振型加入高斯分布的噪音,模拟实际测量误差。通过数值算例研究分析了模态应变能变化率法的抗噪音性能,为Timoshenko梁的损伤识别做了前期准备工作。针对功能梯度Timoshenko梁结构,采用模态应变能变化率法进行结构损伤识别的研究。基于功能梯度Timoshenko梁理论,推导了2节点6自由度梁单元的模态应变能表达式,并给出了表达式中单元刚度矩阵的显式积分。采用功能梯度Timoshenko梁的有限元分析方法,求出模态振型,在此基础上,构建了功能梯度Timoshenko梁结构损伤的识别方法。在损伤识别过程中,由大型商用有限元分析软件ABAQUS计算得到的模态振型加入高斯分布的噪音,模拟振型的测量误差,并讨论了测量误差对损伤识别结果的影响。数值算例表明,模态应变能变化率法可较好地识别出Timoshenko梁结构损伤位置且有较好的抗噪音性能。针对于功能梯度梁结构,分别采用基于Euler-Bernoulli梁理论和Timoshenko梁理论的有限元方法进行振动分析,比较两种模型计算模态振型的差异,讨论这些差异对损伤识别结果的影响,并进一步考虑模态振型测量误差。结果表明跨高比为20左右时,两种模型误差最小,且测量误差的存在使大多数的损伤识别指标值减小。
[Abstract]:FGMs is a new type of heterogeneous composite material whose properties and functions change continuously along the space direction. There is no obvious interface inside the material. These unique advantages of functionally graded materials make it widely used in aeronautics and astronautics. Civil engineering, mechanical engineering, chemical engineering and many other fields have been widely used. The damage of functionally graded materials (FGM) structures is very important because of the damage of structures caused by various factors, even disasters due to the loss of stability, which endangers the safety of life or loses a large amount of property. Based on the functionally gradient Euler-Bernoulli beam theory, the modal strain energy expression of the 2-node 6-DOF beam element is derived, and then the damage identification of the Euler-Bernoulli beam structure is carried out by using the modal strain energy change rate method. In the process of damage identification, the modal mode obtained by finite element method is added to the noise of Gao Si distribution, and the actual measurement error is simulated. The anti-noise performance of modal strain energy change rate method is analyzed by numerical example, and the preliminary work for damage identification of Timoshenko beam is made. The damage identification of functionally gradient Timoshenko beam structures is studied by means of modal strain energy change rate method. Based on the functionally gradient Timoshenko beam theory, the modal strain energy expression of 2-node 6-DOF beam element is derived, and the explicit integral of the element stiffness matrix in the expression is given. The modal modes of functionally graded Timoshenko beams are obtained by using the finite element analysis method. On the basis of this, the damage identification method of functionally graded Timoshenko beams is constructed. In the process of damage identification, the modal modes calculated by the commercial finite element analysis software ABAQUS are added to the noise of Gao Si distribution to simulate the measurement errors of the modes, and the influence of the measurement errors on the damage identification results is discussed. Numerical examples show that the modal strain energy change rate method can identify the damage location of Timoshenko beam structure and has better noise resistance. The finite element method based on Euler-Bernoulli beam theory and Timoshenko beam theory is used to analyze the vibration of functionally graded beam structures. The difference of modal modes calculated by the two models is compared, and the effects of these differences on the damage identification results are discussed. The error of modal mode measurement is further considered. The results show that when the ratio of span to height is about 20, the error of the two models is the least, and the existence of the measurement error reduces most of the damage identification index values.
【学位授予单位】：广西大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O346.5;TB33

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