研究了含有环向表面裂纹损伤的无限长圆柱壳中的波传播和振动功率流特性。用Flügge方程来描述圆柱壳的振动。对于裂纹损伤圆柱壳,运用断裂力学的理论,考虑到裂纹的张开、滑移和剪切三种状态建立了裂纹区域的局部柔度矩阵,得到由此引起的附加广义位移和壳体中内力之间的关系。根据裂纹两侧区域的位移和内力的连续性条件得到了四支反射波和四支透射波的幅值,继而求得壳体中各内力传播的功率流。分析了透射功率流、反射功率流与激励频率和裂纹尺寸之间的联系。文中的研究为基于振动功率流方法识别圆柱壳表面损伤提供了理论基础。
The power flow characteristics of infinite cylindrical shells with circumferential surface crack are investigated.The vibration of the shell is described by FlOgge's shell equation.Considering the three modes of crack, the local compliance matrix at the cracked region is deduced by using the fracture mechanics,and the relationship between the additional generalized displacements and the inner forces is obtained consequently.According to the continuous conditions of displacements and inner forces at the both sides of the crack,the amplitudes of the reflected wave and transmitted wave are obtained,and then the power flow carried by the inner forces is calculated. The relationships among the transmitted and reflected power flow, the crack's depth and driving frequency are researched.The numerical results indicate that the transmitted power flow and reflected power flow are highly related to the crack's parameter. This research provides the theoretical basis for the further crack detection in cylindrical shells based on the vibrational power flow method.