Lowe M J S, Cawley P, Kao J Y, Diligent O
Department of Mechanical Engineering, Imperial College, London SW7 2BX, United Kingdom.
J Acoust Soc Am. 2002 Dec;112(6):2612-22. doi: 10.1121/1.1512702.
An analysis of the reflection of the fundamental Lamb mode a0 from surface-breaking rectangular notches in isotropic plates is presented. The results are obtained from finite element time domain simulations together with experimental measurements. Good agreement is found between the simulations and the measurements. Results are shown for a range of notch widths and depths, including the special case of a crack, defined as a zero-width notch. The reflection coefficient, when plotted as a function of the notch width, exhibits a cosinusoidal periodic shape, and this is explained by interference between the separate reflections from the start and the end of the notch. The reflection coefficient, when plotted as a function of notch depth, shows that in general the reflection increases with both frequency and notch depth, but the shapes of the functions are complex and there are some surprising features. An analysis of the reflection from cracks using the S-parameter scattering approach and some simplified descriptions of the crack-opening behavior yields physical explanations of the nature of these reflection functions. It is found that opening of the crack can be described adequately by a quasistatic assumption only when the crack is small, and in other cases a ray theory approach is more representative. The reflection function is shown to be a result of contributions from both the axial stress and the shear stress in the wave, and the relative importance of these varies with the crack depth and the frequency.
本文对各向同性板中表面开口矩形缺口对基本兰姆波a0的反射进行了分析。结果通过有限元时域模拟和实验测量获得。模拟结果与测量结果吻合良好。给出了一系列缺口宽度和深度的结果，包括定义为零宽度缺口的裂纹这种特殊情况。反射系数作为缺口宽度的函数绘制时，呈现出余弦周期性形状，这是由缺口起点和终点的单独反射之间的干涉所解释的。反射系数作为缺口深度的函数绘制时，表明一般来说反射随频率和缺口深度的增加而增加，但函数形状复杂且存在一些令人惊讶的特征。使用S参数散射方法对裂纹反射进行分析，并对裂纹开口行为进行一些简化描述，对这些反射函数的性质给出了物理解释。结果发现，只有当裂纹较小时，裂纹开口才能通过准静态假设得到充分描述，而在其他情况下，射线理论方法更具代表性。反射函数表明是波中轴向应力和剪应力共同作用的结果，且它们的相对重要性随裂纹深度和频率而变化。
