含环向表面裂纹圆柱壳的波传播特性研究

研究了振动波在含有环向表面裂纹的无限长圆柱壳中的传播特性.圆柱壳体的振动用Flügge方程来描述.运用线弹性断裂力学的理论,考虑到裂纹的张开、滑移和撕裂3种模式以及它们相互之间的耦合,利用分布的线弹簧来模拟裂纹并建立了裂纹所在区域的局部柔度矩阵,得到由此引起的附加位移和壳体中内力之间的关系.在入射波已知的情况下,根据裂纹两侧区域的位移和内力的连续性条件得到了反射和透射波的幅值系数.分析了入射波通过裂纹后的透射、反射系数与激励频率和裂纹尺寸之间的关系.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.

WAVE PROPAGATION CHARACTERISTICS OF CYLINDRICAL SHELLS WITH CIRCUMFERENTIAL SURFACE CRACK

In this paper, the wave propagation characteristics of infinite cylindrical shells with circumferential surface crack are investigated. The vibration of the cylindrical shell is described by Flugge's shell equations and the wave propagation approach is used to solve the equations. In consideration of the crack's three modes: opening, sliding and tearing modes and their combinations, the surface crack is modeled by distributed line springs. The local compliance matrix at the cracked region is then deduced by using linear elastic fracture mechanics, and the relationships between the additional general displacements and the general forces are obtained. To verify the accuracy of the theoretical model and the wave propagation method proposed, the axisymmetric free vibration of a finite shell with a circumferential surface crack is investigated first, the natural frequencies of the finite cracked shell are calculated by using the analytical method and finite element method, respectively. The results between the two methods show a good agreement. Then an infinite shell with a circumferential surface crack is investigated. For a given incident wave, the amplitudes of the reflected wave and transmitted wave are obtained according to the continuity conditions of displacements and inner forces at both sides of the crack. The relationships between the transmitted wave coefficient and the crack's depth as well as the frequency are obtained. The numerical results indicate that the existence of the crack changes the vibration wave in the shell substantially and the amplitudes of the transmitted wave and reflected wave are closely related to the crack's depth and the frequency. The results also show that the coefficients of the transmitted wave decrease with the increase of the crack's depth. This research provides a theoretical basis for the further crack detection in cylindrical shells based on the vibration method.