裂纹圆盘的动态分形特征及裂纹诊断识别

运用有限元方法对裂纹圆盘进行了动态分析，获得了其振型和位移响应；应用多重分形理论计算和分析了裂纹圆盘的振型、位移响应的广义维数和敏感维数，把广义分形维数、敏感维数作为裂纹圆盘故障的特征量，对裂纹圆盘的裂纹诊断与识别进行了定性及定量研究；针对裂纹圆盘的振型、位移响应的广义维数，提出在局部范围内，用局部线性法对圆盘裂纹长度进行定量识别，得到了定量识别裂纹长度的计算公式，通过实例计算考查了裂纹长度的计算精度。分析计算表明，用局部线性法对裂纹长度进行定量识别具有一定的实用性。

Dynamic Fractal Characteristics and Crack Diagnosis and Identification for Crack Disk

The dynamic performance of a crack disk was analyzed by using the finite element method. The vibration mode and displacement of the disk were obtained. The generalized dimension and sensitive dimension of the vibration mode and displacement for the crack disk were calculated and analyzed by using multi-fractal theory. The generalized fractal dimension and sensitive dimension were as fault characteristics of the crack disk, the crack diagnosis and identification for the crack disk had been studied qualitatively and quantitatively. Based on the generalized dimension of the vibration mode and displacement for the crack disk, in the local range, the local linearity method which can quantitatively diagnose the length of the crack disk was put forward. The calculation formula which can quantitatively diagnose the crack length was obtained. By this formula, the crack length can be calculated and obtained. In the light of actual examples, the crack lengths both of calculated and actually measured were compared. The analysis and calculation prove that the local linearity method has its practicability for quantitatively identifying the crack length.