Role of transducer inertia in generation, sensing, and time-reversal process of Lamb waves in thin plates with surface-bonded piezoelectric transducers

Abstract

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.