The Lamb wave time-reversal method has been widely proposed as a baseline-free method for damage detection in thin-walled structures. Under varying thermal environments, it would require that the time reversibility of Lamb waves is temperature invariant. In this study, we examine the temperature dependence of Lamb waves and its time reversibility using experiments and finite element simulations on isotropic plates with surface-bonded piezoelectric wafer transducers for actuation and sensing. The study is conducted at three different temperatures of the system from 25°C to 75°C for a wide range of excitation frequency. The results indicate that the time reversibility can undergo significant changes due to temperature variations depending on the excitation frequency. However, at the best reconstruction frequency corresponding to the maximum similarity of the reconstructed signal with the original input signal (proposed recently as the probing frequency), the change in the percent similarity with temperature is insignificant. The results also demonstrate that changes in the physical properties of both adhesive layers and piezoelectric transducers with temperature play a dominant role in influencing Lamb wave amplitudes. However, only the change in the characteristics of the adhesive layers is responsible for the temperature dependence of the time reversibility of Lamb waves.
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.
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