矩形梁裂纹柔度测量方法研究

摘要

为了描述裂纹引起的矩形梁结构损伤程度,提出了一种基于固有频率的裂纹柔度测量方法.首先通过动力学分析求解矩形梁的前3阶固有频率,建立对应于不同裂纹位置和裂纹柔度的固有频率数据库,并将其拟合为固有频率影响曲面.然后对矩形梁进行振动测试,利用获得的前3阶固有频率去截取固有频率影响曲面,绘制出前3阶频率影响曲线,基于3条频率影响曲线的交点可以得到裂纹柔度和裂纹位置.研究结果表明该方法可以有效地测量出裂纹柔度及对应的裂纹位置.从测量过程可以看出,求解固有频率数据库的输入参数是一系列包含裂纹位置和裂纹柔度的样本点,并没有涉及裂纹的类型 、形状以及裂纹柔度的计算公式.因此,该方法适用于矩形梁中不同类型和形状裂纹的柔度测量,对于含裂纹的梁结构的动力学分析和损伤识别研究具有重要的参考意义.%In order to describe the degree of the structure damage which caused by the crack in the rectangular beam ,a method for measuring the crack flexibility based on the natural frequencies is presented .Firstly ,the first three order natural frequencies of the rectangular beam were resolved by dynamics analysis ,the natural frequency database with various crack locations and flexibilities was set up ,and then the surface-fitting technique was employed to draw the natural frequency in-fluence surfaces .Secondly ,the vibration signal of the rectangular beam was tested ,and the first three order natural frequencies could be obtained .Thirdly ,these frequencies measured were a-dopted to cut the natural frequency influence surfaces ,and then the first three order natural fre-quency influence curves were drawn .The intersection points of these frequency influence curves could indicate the crack flexibility and the corresponding crack location .The results showed that the presented method could effectively measure the crack flexibility and the corresponding crack location .Furthermore ,it could be seen from the measurement process of the crack flexibility that the input parameters for drawing the natural frequency influence surface were a series of sample points of the crack locations and flexibilities .These input parameters had no relation to the type of crack ,the shape of crack and the calculation formula of the crack flexibility .It can be conclu-ded that the presented method can be used to measure the flexibility of the crack with different type and shape in the rectangular beam and can provide an important reference for the study of the dynamics analysis and damage identification of the beam with crack .