Analytical solution for Lamb wave generation and sensing in thin plates through adhesively bonded flexoelectric transducers

Despite numerous studies on flexoelectric devices for actuation, sensing, and energy harvesting applications, their potential for generating and sensing guided waves in thin-walled structures has been largely unexamined. This article presents a theoretical model for the actuation and sensing of Lamb waves in thin isotropic plates, utilizing physically modelled adhesively bonded flexoelectric transducers. The model incorporates shear and peel stresses in the bonding layers to facilitate stress transfer between the transducers and the host plate. The tractions induced by the actuator onto the plate surface are determined by modelling the actuator and plate as Kirchhoff plates. The Lamb wave response of the plate is obtained using elasticity theory in the wavenumber domain spatially and frequency domain temporarily, then converted to space and time domains using the residual theorem and inverse Fourier transform. The strain transfer from the plate to the flexoelectric sensor, along with the resulting electric potential, is evaluated utilizing Kirchhoff plate theory assumptions for the sensor and the plate. For validation, the longitudinal strain at the substrate’s top surface is compared with ABAQUS’ continuum-based finite element results. Numerical studies are presented to demonstrate the influence of the electric field gradient and the thickness of the transducer and adhesive on the time- and frequency-domain Lamb wave response of the plate and the sensor output. The characteristics of the Lamb wave signals produced by flexoelectricity and piezoelectricity are illustrated. The developed model is crucial for realizing applications of flexoelectric materials in material characterization, medical diagnosis, and structural health monitoring.