Extension of the Crawley’s adhesive model to dynamically actuated piezoelectric transducers

“Use of piezoelectric actuators as elements of intelligent structures” is a classic article authored by Crawley and De Luis originally published in the AIAA Journal in 1987. The article provides an elegant one-dimensional model describing the behavior of piezoelectric transducers bonded to a structure, including the effect of the adhesive film. The use of the Crawley’s solution is widespread and up-to-date the model accounts for thousands of citations. This article discusses some of the limitations of the Crawley model and offers a simple, yet more generic solution to the problem by considering the inertia term in the piezoelectric transducer. Although omitted in the original work, this article shows that near the transducer’s resonance, the shear stress distribution at the interface between the adhesive and the substrate might be substantially dissimilar from the one described by Crawley and De Luis. In particular, for either relatively high frequencies or for soft adhesive films, the Crawley equation does not provide an accurate model to the transducer/substrate coupling. Finally, in this work we present an analytical solution for the dynamic electro-mechanical admittance of the transducer bonded to the substrate. A simple finite element method validation study is also offered to support the findings of the proposed model.