多重分形的智能材料损伤诊断应用
|
摘要
多重分形谱所蕴含的信息比单一的分数维要深刻而全面 ,在解决实际问题中多重分形主要用来描述物理量不均匀的随机概率分布。在智能复合材料有损伤前后其内部状态从平衡到不平衡 ,再到更高层次的平衡过程中受力的空间分布发生变化 ,利用多重分形方法将这一不平衡程度进行量化 ,多重分形谱Dq-q从平缓到陡峭的变化反映了分形结构复杂性的增加 ,反映了材料内部应力分布不均匀性的增加。数据仿真计算结果和对在一块埋置有 5× 5传感光纤阵列的复合材料试件实测数据的计算结果表明该方法的有效性与实用性。
The implication of multi-fractal spectrum is more profound with profusion of information than the simply fractal dimension. In settling the engineering-oriented problems, the multi-fractal spectrum is mainly to describe the random probability distribution of physical phenomenon. Before the damage of structures occurrence, the multi-fractal spectrum of space distribution of interior strain changes from centralized to loose, which indicates that complexity of damage fractal structure and the inhomogeneity of space distribution are both increasing. By studying the numerical simulation of point sets, the conclusion is drawn that the physical essence of multi-fractal spectrums before and after the damage of smart materials and structures occurrence is a ever-changing process from homogeneous to inhomogeneous, from simple to complex. The calculated result upon the data of a specimen, into which fiber sensors network is embedded and its size is 5×5 (units), indicates that the diagnosis method is reliable and practical.
The implication of multi-fractal spectrum is more profound with profusion of information than the simply fractal dimension. In settling the engineering-oriented problems, the multi-fractal spectrum is mainly to describe the random probability distribution of physical phenomenon. Before the damage of structures occurrence, the multi-fractal spectrum of space distribution of interior strain changes from centralized to loose, which indicates that complexity of damage fractal structure and the inhomogeneity of space distribution are both increasing. By studying the numerical simulation of point sets, the conclusion is drawn that the physical essence of multi-fractal spectrums before and after the damage of smart materials and structures occurrence is a ever-changing process from homogeneous to inhomogeneous, from simple to complex. The calculated result upon the data of a specimen, into which fiber sensors network is embedded and its size is 5×5 (units), indicates that the diagnosis method is reliable and practical.
引文
[1]陈 禺页,陈 凌.分形几何学[M ].北京:地震出版社,1998:125-137.
[2]杜善义.复合材料细观力学[M ].北京:科学出版社,1998.
[3]张济忠.分行[M ].北京:清华大学出版社,1995:328-335.
[4]何 锬,彭 文.分形几何学在微结构研究中的运用[J].西南石油学院学报,2000,5.
[5]ChbabraA ,JensenRV .Directdeterminationonthef(α)singularityspectrum[J].PhysReviewLetters,1989,62(12):1327-1330.
[6]杨 红.空心光纤用于智能结构自诊断、自修复的研究[D].南京:南京航空航天大学,2001.
[7]王炳武,胥 讠胥.MATLAB 5.3实用教程[M ].北京:中国水利水电出版社,2000.
[2]杜善义.复合材料细观力学[M ].北京:科学出版社,1998.
[3]张济忠.分行[M ].北京:清华大学出版社,1995:328-335.
[4]何 锬,彭 文.分形几何学在微结构研究中的运用[J].西南石油学院学报,2000,5.
[5]ChbabraA ,JensenRV .Directdeterminationonthef(α)singularityspectrum[J].PhysReviewLetters,1989,62(12):1327-1330.
[6]杨 红.空心光纤用于智能结构自诊断、自修复的研究[D].南京:南京航空航天大学,2001.
[7]王炳武,胥 讠胥.MATLAB 5.3实用教程[M ].北京:中国水利水电出版社,2000.
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心