基于小波有限元的结结裂纹参数识别

发布时间：2018-05-29 20:24

本文选题：小波有限元 + 悬臂裂纹梁　；参考：《华中科技大学》2011年硕士论文

【摘要】：结构裂纹的出现和在交变应力作用下的不断扩展,容易造成结构的破坏进而导致重大安全事故的发生,因此在早期对裂纹进行定量识别以保证结构安全在工程实际中具有重要意义。振动诊断法因其方便、快速的特点在工程故障诊断中应用广泛,小波有限元因其多分辨率分析的特性在处理裂纹等奇异性问题上精度较高,因此本文研究基于小波有限元的悬臂裂纹梁参数辨识问题。首先,计算了Daubechies小波尺度函数和联系系数,推导并计算了Coiflet小波尺度函数和联系系数,将小波多分辨分析的特性通过尺度函数作为插值函数引入有限元,构造了Daubechies小波梁单元和Coiflet小波梁单元,并通过算例验证了小波梁单元在梁弯曲问题和振动问题中具有很高精度。然后,将裂纹视为无质量扭转线弹簧,建立悬臂裂纹梁的小波有限元模型,求解不同裂纹参数下悬臂梁的前三阶固有频率,与解析解吻合程度很高,验证了悬臂裂纹梁小波有限元模型在裂纹辨识正问题中的有效性;采用等高线法,将实测固有频率作为裂纹辨识反问题的输入,利用实测固有频率等高线投影线的交点进行裂纹深度和位置的识别,通过文献中给出的实测固有频率成功进行了裂纹辨识,验证了悬臂裂纹梁小波有限元模型在裂纹辨识反问题中的有效性。最后,进行了悬臂裂纹梁激振实验,利用实验测得的固有频率进行基于小波有限元模型的悬臂裂纹梁参数辨识,取得了很好的效果。
[Abstract]:The appearance of structural cracks and the continuous expansion under the action of alternating stress can easily lead to the destruction of the structure and lead to the occurrence of major safety accidents. Therefore, quantitative identification of cracks in early stage to ensure structural safety is of great significance in engineering practice. Vibration diagnosis method is widely used in engineering fault diagnosis because of its convenience and rapidity. Wavelet finite element method has high accuracy in dealing with singularity problems such as cracks because of its multi-resolution analysis. So the parameter identification of cantilever crack beam based on wavelet finite element method is studied in this paper. Firstly, the scaling function and the contact coefficient of Daubechies wavelet are calculated, and the scaling function and contact coefficient of Coiflet wavelet are deduced and calculated. The characteristics of wavelet multi-resolution analysis are introduced into finite element method by scaling function as interpolation function. The Daubechies wavelet beam element and the Coiflet wavelet beam element are constructed, and the results show that the wavelet beam element has a high accuracy in the bending and vibration problems of the beam. Then, the crack is regarded as a massless torsion line spring, and the wavelet finite element model of the cantilever crack beam is established. The first three natural frequencies of the cantilever beam with different crack parameters are solved, which is in good agreement with the analytical solution. The validity of the wavelet finite element model of cantilever crack beam in the positive problem of crack identification is verified, and the measured natural frequency is used as the input of the inverse problem of crack identification by using the contour method. The crack depth and position are identified by using the intersection point of the measured natural frequency contour projection line, and the crack identification is successfully carried out through the measured natural frequency given in the literature. The validity of the wavelet finite element model of cantilever crack beam in the inverse problem of crack identification is verified. Finally, the vibration experiment of cantilever cracked beam is carried out, and the parameter identification of cantilever crack beam based on wavelet finite element model is carried out by using the natural frequency measured in the experiment, and good results are obtained.
【学位授予单位】：华中科技大学
【学位级别】：硕士
【学位授予年份】：2011
【分类号】：TH165.3

【引证文献】