基于模态应变能方法功能梯度材料梁式结构损伤识别的研究

Functionally graded material(FGM) is a new kind of inhomogeneous composite materials with the continuously varying material property in space. As a very improtant structural component in engineering, FGM beam-like structures have been increasingly used in many fields, such as aerospace, civil engineering, etc.,due to their unique graded feature. Damage in the FGM beam-like structures will reduce the system safty performance. Without finding the accumulating continually damage in such strucutres during their service life, there probably occurs a catastrophic structural failure, which will result in heavy losses. Therefore, it is inevitable to identify the damage in the FGM beam-like structures for FGM application in modern engineering. Damage identification method which is based on modal strain energy has superior in many respects such as the sensitivity to local defects, severity estimation, stability and noise resistance ability. This project intends to study the damage identification of FGM beam-like structures based on modal strain energy method. A finite element model with higher accuracy will be developed for the dynamic analysis of FGM beam-like structures by considering the higher-order shear deformation beam theory. On the basis of the hihger-accuracy finite element model, hypersensitivity indicators for the damage identification of the FGM beam-like structures will be designed by way of modal strain energy method. The probabilities of indicators for the damage identification will be considered to investigate the probability problem of the damage identification and false alarm, which will reduce false positive rate and false negative rate. Furthermore, the factors that influence the identified results of damage will be probed from different angles, such as model errors, noise, the number of mode shapes and so on.

功能梯度材料是一种材料性能连续变化的新型非均匀复合材料。作为工程中很重要的构件，功能梯度材料梁式结构在航空航天、土木工程等领域有独特的应用。该类结构损伤时，会影响整体结构的安全性能。没有注意到损伤发生并不断累积的情况，而继续使用这类结构，最终会导致结构失效，造成重大损失。因此，功能梯度材料梁式结构损伤识别已成为其应用的必然要求。模态应变能损伤识别方法在局部损伤的敏感度、识别损伤的程度、稳定性和抗噪音等方面有优势。本项目拟进行基于模态应变能方法功能梯度材料梁式结构损伤识别的研究。基于高阶剪切变形梁理论，建立功能梯度材料梁式结构动力分析的高精度有限元数值模型。在此基础上，基于模态应变能方法提出结构损伤识别的高敏感度量化指标。引入损伤量化指标的统计概率，研究结构损伤识别和虚警(false alarm)的统计概率问题，减少损伤误报率和漏报率，并探讨模型误差、噪音，振型阶数等因素对识别结果的影响。

功能梯度材料是一种材料性能连续变化的新型非均匀复合材料。功能梯度材料梁式结构是工程应用中很重要的构件，该类结构的损伤识别是重要的研究课题。基于模态应变能的损伤识别方法在局部损伤的敏感度、识别损伤的程度、稳定性和抗噪音等方面有优势，是一种重要的方法。本项目围绕功能梯度复合材料结构的相关问题，进行复合材料结构的理论分析，建立高精度和高效率的复合材料结构数值计算模型。在此基础上，基于模态应变能方法，研究功能梯度材料梁式结构损伤识别的问题。针对功能梯度材料梁式结构，研究结构损伤识别的高敏感度量化指标问题，探讨损伤识别统计概率问题的解决方法，并探讨模型误差、噪音，振型阶数等因素对识别结果的影响。基于基于Timoshenko梁理论和高阶剪切变形梁理论，将达朗贝尔原理运用到虚功原理中，推导得出功能梯度Timoshenko梁和高阶剪切梁振动分析的有限元计算格式。通过与文献解析解对比，验证了功能梯度Timoshenko梁和高阶剪切梁有限元格式和梁单元的精确性和适用性。基于模态应变能变化率定义结构损伤识别指标，并构建了功能梯度材料梁损伤识别方法。数值算例表明，该方法可较好地识别出功能梯度梁结构损伤位置且有较好的抗噪音性能。推导出了功能梯度材料Euler-Bernoulli梁、Timoshenko梁和高阶剪切梁的刚度矩阵和线性系统的单元模态应变能一阶灵敏度解析表达式。然后，基于单元模态应变能灵敏度和泰勒公式推导了功能梯度i梁的损伤识别方程组，利用Tikhonov正则化和L曲线方法，求解上述损伤方程组，最后，针对实际工程中诸多的不确定性问题，引入概率统计方法，解决单元损伤存在的概率问题。根据损伤存在概率的大小判别单元是否发生损伤。结果显示损伤单元的损伤存在概率为1，未损单元损伤存在概率为0.05。同时讨论了噪音水平、损伤程度、边界条件对识别效果的影响。本项目的工作为今后的进一步研究打下良好的基础，同时也为功能梯度复合材料结构展示了良好的应用前景。