Modelling of a cantilever non-symmetric piezoelectric bimorph

The aim of this paper is the modelling of a non-symmetric bimorph constituted by a piezoelectric material deposited on an alumina substrate and used either as an actuator or a sensor. Theoretical modelling based on the flexural modes of the structure is carried out and the influence of the electrode characteristics (geometrical dimensions and elastic parameters) is introduced in the modelling for calculating the bimorph bending displacement. In actuator mode, the electrical admittance of the cantilever non-symmetric bimorph is stated and the intrinsic electromechanical coupling factor linked to the bimorph bending motion is deduced and compared with that defined in IEEE Standards. The analytical modelling was used for characterizing a cantilever bimorph constituted by a piezoelectric thick film deposited on an alumina substrate. A trial and error fitting method is described for determining the elastic, piezoelectric and dielectric constants of the piezoelectric material. The influence of the electrode parameters is calculated and the measurement uncertainty is deduced. In sensor mode the open voltage delivered by the bent piezoelectric layer and the electrical equivalent circuit of the bimorph are given. Theoretical results are compared with those obtained by the finite element method, and discussed.