F. Lalande et al., A SIMPLIFIED GEOMETRICALLY NONLINEAR APPROACH TO THE ANALYSIS OF THE MOONIE ACTUATOR, IEEE transactions on ultrasonics, ferroelectrics, and frequency control, 42(1), 1995, pp. 21-27
A simplified model for the analysis of ceramic-metal composite actuato
rs has been developed, The model consists of two beams symmetrically a
rranged about the actuator neutral axis and attached to the actuator a
t the ends with an offset (Moonie shape). When an electrical field is
applied such that the actuator will contract, a compressive force and
a moment, due to the beams' eccentricity, are applied to the beams, Th
is loading will produce the desired deformation of the beams, Using th
e beam-column theory and the appropriate boundary conditions, it is po
ssible to derive a set of equations relating the free induced strain (
Lambda) of the actuator to the midspan displacement of the beams. Nonl
inear terms which allow for the interaction of the developed in-plane
force with the out-of plane displacements have been included in the eq
uations. Applying these equations to a particular case, it is found th
at the offset distance of the beams has a large impact on the behavior
of the system. An increase in the offset distance produces both a sui
table augmentation of the moment applied to the beams and an undesirab
le diminution of the midspan displacement for a given free induced str
ain, From these two positive and negative effects, an optimum value of
the offset distance is found. Additionally, it is found that with a t
ransverse load applied to the beams, the optimum offset distance is fu
rther increased, Furthermore, the nonlinear terms in the governing equ
ations are found to have only a small impact on the system in the free
induced strain range of typical actuator materials, i.e., Lambda less
than or equal to 1500 mu strain. Thus, in conclusion, the effect of t
he offset distance of the beams to the actuator is the primary design
criteria when maximum displacement of the actuator is required.