Dynamic modelling and analysis of V- and Z-shaped electrothermal microactuators

This paper presents a dynamic model and design analysis for V- and Z-shaped electrothermal microactuators operating in vacuum and in air conditions. The model is established with a coupled-field analysis combining the electrothermal and thermomechanical analyses for both heating and cooling processes. The electrothermal behaviors that dominated the overall dynamics are described by hybrid partial differential equations for three serially connected segments. The equations are solved subjected to the boundary, continuity, and initial conditions, and a unique method based on Fourier series is utilized to solve the temperature increase in each arms. The thermomechanical responses, i.e., the displacement and force, of the actuator are then calculated under the assumptions of quasi-static inertia. The analytical evaluations of the temperature and displacement are compared with the ones from finite element analysis via ANSYS software. A good agreement is found between analytical and simulation results. By virtual of the finite-element simulation, local high-frequency low-amplitude vibrations are demonstrated along the overall dynamic response for both V- and Z-shaped actuators with specific dimensions. Moreover, distinct dynamic behaviors between U- and V- and Z-shaped beams are observed and discussed using a proposed comparison benchmark. Finally, based on the dynamic model, the influences of structural as well as material parameters on the dynamic behaviors are analyzed to pave the way for improving the design and optimizing the dimensions of V- and Z-shaped electrothermal microactuators.