Admittance matrix of a trapezoidal piezoelectric heterogeneous bimorph

Bimorph structures are a standard method for transforming the high force of piezoelectric materials into a large deflection. In micro electromechanical systems (MEMS) applications, it is preferable to use structures consisting of a passive substrate (usually silicon) and one or more piezoelectric layers on the top. Such structures are called heterogeneous bimorphs or enakemesomorphs. In some MEMS applications- for example, for use as acoustic transducers-it is desirable to arrange such heterogeneous bimorphs in a circular shape, which results in trapezoidal cantilever structures. In this paper, an analytic dynamic description of such actuators is obtained. The resulting model is proved to be compatible with existing models for heterogeneous bimorphs with constant width. A comparison to a finite element analysis model of an exemplary layout shows divergences wholly within the same range as found for published models for constant-width structures.