裂纹梁动态响应有限元分析中的线弹簧模型

本文提出了一种以线弹簧模型为基础来分析裂纹梁动态响应的新数值方法．应用能量原理和断裂力学理论首次建立了线弹簧模型的刚度矩阵，从而确立了一种能使二维裂纹问题转化为一维分析的梁的有限元模型．使用这个模型，研究了不同裂纹长度和裂纹位置对悬臂梁固有频率和振型的影响，并把计算所得到的数值结果与现有的实验数据作了比较．结果表明，当无量纲裂纹长度小于０．６时，两者吻合得非常好；反之，两者之间存在较大的误差．对这种误差产生的原因，本文也作了解释．

A LINE-SPRING MODEL IN FINITE ELEMENT ANALYSIS OF DYNAMIC RESPONSES OF A CRACKED BEAM

In this paper a new numerical method based on a line-spring model is developed to analyze the dynamic response of a cracked beam. A stiffness matrix of the linespring model is first derived using the energy principle in conjunchon with fracture mechanics method. A finite element model of a cracked beam is then established which enables a onedimensional analysis of a two-dimensional crack problem. The effects of natural frequencies and the corresponding mode shapes are investigated for a cracked cantilever beam with differentcrack lengths and crack positions using the model. The comparisons between the numericalresults and the available experimental data are made. It is shown that both are very agreeable when the non-dimensional lengths of crack are less than 0.6; on the contrary, there are greater discrepancies between them. The causes of the errors are interpreted.