Modeling of Beam Electrothermal Actuators

Beam electrothermal actuators amplify the thermal expansion of pre-shaped beams and use the symmetrical structure to create a linear motion. These actuators, including V and Z shapes, are widely used in microsystems. Explicit analytical expressions are derived in this paper governing the structural deformation of these actuators due to electrothermal expansion and interaction with external lateral load. The analytical expressions are developed for an arbitrary initial shape of the actuator beams with symmetry and uniform cross-section. The modeling is based on the elastic beam theory, and all the modes of buckling are considered in the analytical solution. The solution and analytical expressions account for axial forces in tension and compression. The modeling considers the buckling with the third mode, which occurs at a certain limit of the axial compression and leads to significant variation in the stiffness of the actuator. This phenomenon is well studied for bistable pre-shaped beams, but related studies are limited for beam electrothermal actuators. As a case study, the V shape actuator is specifically investigated. The modeling shows very good agreement with finite element simulations and experimental data based on micro-machined in-plane silicon actuators.