The Force-Deflection Behavior of Functionally Graded Piezoceramic Actuators

Functionally Graded Piezoceramics (FGP) overcome the current reliability limitations within laminated piezoceramic actuators by eliminating the bond lines and stress discontinuities and lowering the overall internal stress levels. New fabrication methods for FGP, such as the Dual Electro/Piezo Property (DEPP) gradient technique, synergistically couple variations in permittivity and piezoelectric properties yielding more electrically efficient actuators capable of larger displacements. Unfortunately, such FGP approaches naturally introduce complexity into the electric field, stress, and material profiles, making it more difficult to model their performance. This paper develops a Hamiltonian energy-based modeling approach that fully captures the force-deflection performance of a generic multidimensionally graded piezoceramic actuator. As demonstration of the approach, two differently graded beams are presented: a two layered gradient that maximizes deflection and a linear gradient that minimizes internal stresses. DEPP graded prototypes were fabricated with a powder-pressed method for the two-layered specimen and microfabrication via co-extrusion for the linear gradient. The force-deflection performance of each cantilevered prototype under tip loading conditions was experimentally and numerically validated. The derived analytic model correlates very well with the observed behavior by incorporating the complex electric field variation and continuous stress distribution within the prototype eluded by conventional modeling methods. This comprehensive quasi-static force-deflection model provides designers with an effective and necessary tool for the implementation of FGP as actuators with extended service lifetimes.

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