Dynamic Shear-Lag Model for Stress Transfer in Piezoelectric Transducer Bonded to Plate

Abstract

Crawley and Luis (“Use of Piezoelectric Actuators as Elements of Intelligent Structures,” AIAA Journal, Vol. 25, No. 10, 1987, pp. 1373–1385) presented in the year 1987 a classic one-dimensional (1-D) quasi-static shear-lag model for the stress transfer between piezoelectric actuators and the host beam to which they are bonded through adhesive layers. Since then, it has been the backbone in modeling piezoelectric actuation and sensing. However, even after 30 years of its existence, the model remains to be extended to incorporate the inertia terms of the system, which is important for high-frequency applications, such as structural health monitoring. This work presents a consistent and generic extension of the 1-D shear-lag model for the dynamic stress transfer of a piezoelectric wafer transducer bonded to a thin isotropic plate, incorporating the inertia of the transducer, host plate, and the adhesive. The transducer and the plate were considered to be under plane strain condition. The plate was modeled using the classical Kirchhoff’s plate theory, whereas the wafer transducer was considered to undergo only extensional deformation. The model led to a simple closed-form solution for the shear stress induced at the transducer–plate interface under harmonic electric potential excitation. The results were compared with detailed two-dimensional finite element dynamic simulations. A detailed numerical study was conducted to illustrate the influence of various transducer, plate, and adhesive parameters, as well as the excitation frequency on the inertia effect on the interfacial shear stress.