基于模态振型的圆截面梁裂纹识别等高线法

因在外部载荷的作用下，梁构件内部结构容易发生裂纹的萌生和扩展，甚至导致梁构件发生断裂从而引发灾难性事故，研究一种基于模态振型的圆截面梁裂纹识别等高线法。先推导无裂纹单元与含裂纹单元的刚度矩阵，然后求解含裂纹圆截面梁振动微分方程，发现裂纹工况对模态振型有一定的影响。在此基础上，研究不同裂纹位置比和不同裂纹深度比之下前三阶模态振型突变的响应曲面，提出基于模态振型的裂纹识别等高线法。结果表明:对于单裂纹圆截面梁裂纹识别，裂纹深度和裂纹位置的预测结果误差为0；对于双裂纹圆截面梁裂纹识别，裂纹深度预测最大误差不超过2%，裂纹位置预测最大误差不超过2%。

Contour Line Method of Crack Identification for a Circular Cross Section Beam Based on Modal Shape

Under the action of external loads, crack initiation and propagation are easy to occur in a beam component. The purpose of this article is to study a contour line method of crack identification for a circular cross section beam by the modal shape. Firstly, the stiffness matrix of uncracked element and cracked element is derived. Then, the vibration differential equation of a cracked circular cross section beam is solved. It is found that the crack condition plays a certain role on the modal shape. Thereafter, the first three modal shape mutation response surfaces with different crack position ratios and different crack depth ratios are studied. Subsequently, the contour line method of crack identification based on modal shape is proposed. Results indicate that the prediction error of crack depth and crack position is zero for the crack identification of single cracked circular cross section beam. But the error of crack depth prediction is less than 2%, and the maximum error of crack position prediction is less than 2% for the crack identification of double cracked circular cross section beam.