摘要
裂纹是工程结构中最常见的一种损伤模式,严重威胁着结构的完整性和安全性。基于振动特征的裂纹诊断方法由于具有测试整体性和在线性等诸多特点而受到了广泛的关注和重视。为了实现裂纹的定量辩识,通常的方法是对动力学模型中的裂纹参数通过某种方式加以调整使得计算结果与参考结果间差异最小,最后的裂纹参数即为辩识结果。由此可见,裂纹的定量辩识对动力学计算模型和裂纹参数搜索两方面的效率要求非常高,关系到其在工程实际中是否具有应用价值。论文的主要目的就是在基于振动信号的裂纹故障诊断理论框架下,研究提出精确而高效的动力学分析模型与裂纹辩识方法,为实现裂纹的在线监测和诊断提供一种切实可行的方案。
论文分析了均质和非均质材料梁中各式裂纹在典型载荷作用下的局部柔度,给出了其显式表达式。提出了基于裂纹集中柔度模型和p型有限元方法的裂纹梁结构动力学特性和响应分析方法。通过与实验值以及常规有限元计算结果的比较表明该方法具有计算精度高、收敛速度快等优点。利用该p型有限元方法研究了在关键领域有广泛应用但以往研究鲜有涉及的几类工程结构,包括几何非均匀梁、材料非均匀梁和旋转变截面梁在出现裂纹前后的动力特性,讨论了相关参数如裂纹深度、裂纹位置、边界条件、高度变化率、材料梯度率、旋转速度等对于其振动特性的影响。
针对单变量型有限元法在计算其它场变量时的精度损失问题,提出了多变量p型有限元方法。该方法以广义变分原理和函数逼近理论为基础,不仅能够同时准确地求解出多个场变量,而且还有很好的收敛性能。该方法可以作为基于应力、应变等变量的结构完整性监测和评估技术的有力支持。
对现代免疫算法在裂纹定量辩识上的应用进行了初步的尝试。提出了一种用于裂纹辩识的改进型目标函数,并通过免疫智能算法对该目标函数模型进行寻优。算例和实验研究表明该方法能够有效地解决裂纹的定量辩识问题。该研究不仅拓宽了免疫算法的应用范围,同时也为裂纹的检测和识别开辟了一种新的途径。
Crack is one of the most common damage of engineering structures, which severely threatens the integrity and security of those structures. The vibration-based diagnosis techniques have been attracted a large number of research interest due to their prominent capabilities, such as they only depend on the global vibration signal and can be implemented in on-line manner. To identify crack parameters quantitatively, the dynamic model of structures should be established firstly and then the possible crack parameters are adjusted such that the difference between the calculated results based on the model containing crack parameters and the reference values is minimal. It can be seen that the efficiency of the dynamic model and the searching of crack parameters is crucial to the practical application of the quantitative crack identification techniques. Thus, the primary purpose of the dissertation is to present accurate and efficient dynamic models and crack identification approaches and provides a feasible scheme for on-line monitoring and diagnosis of cracks.
Local flexibilities of cracks under different loading in homogeneous and non-homogeneous beams are derived firstly. Then a new methodology based on the lumped crack model and the p-version of finite element method (p-FEM) is developed to analyze the vibration characteristics and dynamic response of cracked structures. Comparisons between results by the proposed method and results in the literature and by conventional finite element method (CFEM) show that the p-FEM has superior accuracy and convergent to the CFEM. The proposed method is subsequently applied to analyze the dynamic properties of several kinds of cracked structures which have been widely used in various important engineering fields but received little attention in previous investigation, including geometrical non-uniform beams, physical non-uniform beams and rotating beams. The effect of some parameters such as crack location, crack size, boundary condition, taper ratio, material gradient and rotation speed are discussed.
To avoid the accuracy loss of the rest field variables in the uni-variable finite element method, the multivariable p-FEM on the basis of the generalized variational principle and the function approximation theory is developed. The method can obtain multiple field variables simultaneously with very high precision as well as has excellent convergent, which will promote the application of structural integrity evaluation techniques with stress or strain as their inputs.
As an elementary attempt, the modern immune algorithm (IA) is employed to tackle the quantitative crack identification. An improved objective function is put forward and the IA is used to solve this optimization problem. Numerical and experimental studies demonstrate that this strategy can effectively identify cracks with acceptable accuracy. This present work not only broadens the application fields of the IA, but also provides a novel way to crack detection and identification.
引文
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