In this paper the constituent equations that describe the behavior of a multi-layer piezoelectric cantilever on the coupled electronic and mechanical domain are presented. The study is based on the modal analysis of the partial differential equations governing the motion of an Euler-Bernouilly cantilever beam and on a pair of linearly coupled piezoelectric equations. An important element in the modelization of such materials is the energy loss term, in this paper a viscous damping contribution is considered which allows us to extract a more realistic constituent equations for the material to work as sensor and actuator. The development of this equation as an infinite linear combination of each mode allows us to extract a compact lumped equivalent electrical circuit to work at any frequency region as sensor or actuator instead of the classical reduced models. Theory is reduced to study the dynamics of a triple-layer commercial cantilever and then is compared with experimental results.
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