The effectiveness of a piezoelectric bimorph actuator to perform mechanical work under various constant loading conditions

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Abstract
The equations governing the energy and work relations for a piezoelectric bimorph for various mechanical boundary conditions are derived. The stored energies and external work are calculated for a clamped cantilever bimorph with an antiparallel orientation. The system is subjected to an applied voltage on one side of the beam and three different classical boundary conditions on the other side. These conditions are: a mechanical moment, M, at the end of the beam, a perpendicular force, F, applied at the tip of the beam, and a uniform load, p, across the length of the beam. The stored energies are related to the system through the canonical conjugates of the boundary conditions, namely: an angular deflection, α, a vertical deflection, δ, and a swept volume displacement, V, respectively. Through the use of these relationships the total internal energy supplied to the bimorph is calculated. The work performed by the bimorph on its environment is also calculated. With the stored energies and the work performed known, an over all effectiveness is found. Through the use of this effectiveness a realistic approach to fabrication of devices can be sought.