An analytical model is presented for the generation, sensing, and time-reversible process of Lamb waves in thin isotropic plates with surface-bonded piezoelectric wafer transducers, incorporating the shear-lag effect of the bonding layer and inertia effects of the system in transducer modeling. A one-dimensional dynamic shear-lag model for the actuator-plate interaction is used to obtain the shear stress distribution at the actuator-plate interface. The Lamb wave solution for the plate under this shear traction excitation is obtained using the two-dimensional (2D) elasticity equations. A consistent sensor-plate interaction model incorporating the shear-lag and inertia effects is developed to determine the induced sensor voltage from the Lamb strain at the plate surface. The model is validated by comparing it with the 2D coupled piezoelasticity-based finite element simulation and experimental data. Detailed parametric studies are conducted to illustrate the effect of inclusion of inertia of actuator, sensor, adhesive, and plate in the transducer modeling on the Lamb wave generation, sensing, time reversibility, and the system’s best reconstruction frequency, and to ascertain how various geometrical and material parameters of the system influence the same. The developed closed-form solution will be immensely useful for the design of Lamb wave based structural health monitoring systems.

提出了一种分析模型，用于具有表面粘合压电晶片换能器的各向同性薄板中兰姆波的产生、传感和时间可逆过程，在换能器建模中结合了粘合层的剪切滞后效应和系统的惯性效应. 致动器-板相互作用的一维动态剪切滞后模型用于获得致动器-板界面处的剪切应力分布。使用二维 (2D) 弹性方程获得在这种剪切牵引激励下板的兰姆波解。开发了一个结合了剪切滞后和惯性效应的一致的传感器-板相互作用模型，以确定来自板表面兰姆应变的感应传感器电压。该模型通过与基于二维耦合压电弹性的有限元模拟和实验数据进行比较来验证。进行了详细的参数研究，以说明在换能器建模中包含执行器、传感器、粘合剂和板的惯性对兰姆波生成、传感、时间可逆性和系统最佳重建频率的影响，并确定各种几何形状如何和系统的材料参数影响相同。开发的封闭形式解决方案对于基于兰姆波的结构健康监测系统的设计非常有用。和板在换能器中对兰姆波的产生、传感、时间可逆性和系统的最佳重建频率进行建模，并确定系统的各种几何和材料参数如何影响这些参数。开发的封闭形式解决方案对于基于兰姆波的结构健康监测系统的设计非常有用。和板在换能器中对兰姆波的产生、传感、时间可逆性和系统的最佳重建频率进行建模，并确定系统的各种几何和材料参数如何影响这些参数。开发的封闭形式解决方案对于基于兰姆波的结构健康监测系统的设计非常有用。