Analysis and optimization of loaded cantilever beam microactuators

A review of the design and modelling of cantilever beam microactuators is presented. The structures, fabricated by film technology, often have varying composition in the normal to film plane direction and stress-strain relations easily measurable only in the film plane. In this paper, a simple and straightforward analytical model of the mechanical response of cantilever beam microactuators loaded normally at the tip is presented, considering only the commonly known material properties (stress-strain relations in beam length direction), whereas the material properties may vary continuously in the beam thickness direction. The elastic curve and normal reaction force at the beam's tip are expressed via three integrals over the longitudinal stiffness coefficient of the material and the externally-induced longitudinal free strains. A set of special solutions for two-layer beams, including their optimum dimensions for maximal generated force and tip deflection, but also for some beam structures with continuously varying material properties in the thickness direction, is presented and compared with formerly published data and FEM simulations. Features of the elastic curve of tip normal loaded cantilever beam actuators are analysed. The analogy with passive loaded beam solutions is highlighted. A method for determining the reaction force at the beam's tip by elastic curve parameters is presented.