Theoretical modeling of low-attenuation lamb wave modes generation in three-layer adhesive joints using angle beam transducer

AbstractIn this paper, at first the attenuation of Lamb waves in three-layer adhesive joints, including two elastic plates bonded together by a viscoelastic adhesive layer, is investigated using Global matrix method and then suitable incidence angle is theoretically calculated to generate low-attenuation Lamb waves using angle beam transducer. Theoretical boundary value problem in three-layer adhesive joints with perfect bond and traction-free boundary conditions on their outer surfaces is solved to find a combination of frequencies and modes with lowest attenuation. Characteristic equation is derived by applying continuity and boundary conditions in three-layer joints using Global matrix method. Phase velocity dispersion curves and attenuation intensity plot in high and low frequencies are obtained with numerical solution of this equation by a computer code for a three-layer joint, including an aluminum repair patch bonded to the aircraft aluminum skin by a layer of viscoelastic epoxy adhesive. To validate the numerical solution results of characteristic equation, wave structure curves are plotted for a special mode in two different frequencies in the adhesive joint. Also, transducer incidence angle is calculated in terms of frequency for different modes using theoretical method to generate Lamb wave modes with low attenuation level by angle beam transducer. These modes are recognizable by transducers in inspections with Lamb waves because of low attenuation level.

摘要 本文首先采用全局矩阵法（Global matrix method），研究由粘弹性胶层粘接两块弹性板形成的三层粘接接头中的兰姆波（Lamb waves）衰减特性，随后通过理论计算确定适宜入射角，以利用角束换能器（angle beam transducer）生成低衰减兰姆波。针对外层表面满足完美粘接与无牵引边界条件的三层粘接接头，本文建立理论边值问题（boundary value problem），以筛选出衰减最低的频率与模态组合。通过全局矩阵法应用三层接头的连续性与边界条件，推导得到特征方程（characteristic equation）；针对以粘弹性环氧胶将铝修复补片粘接于飞机铝蒙皮之上的三层接头，借助计算机代码对该特征方程进行数值求解，得到高低频段下的相速度频散曲线（phase velocity dispersion curves）与衰减强度图（attenuation intensity plot）。为验证特征方程数值解的正确性，本文针对该粘接接头中两种不同频率下的特定模态绘制波结构曲线（wave structure curves）。此外，本文基于理论方法推导不同模态下入射角随频率的变化关系，以通过角束换能器生成低衰减水平的兰姆波模态——这类模态因衰减水平极低，在兰姆波检测中可被换能器有效识别。