Vibration Analysis of U-Shaped Beam Electrothermal Microactuators

This paper presents an analytical model for the vibration analysis of a U-shaped electrothermal microactuators. A U-shaped electrothermal microactuator has a unique geometrical structure which consist of, interconnected multiple thick and thin beam segments. In this proposed model, both the longitudinal and lateral deflections of each beam segment are incorporated. To facilitate the modelling process, a thick beam is replaced by the thin beam segment using the artificial Young's modulus and density so that the deformation and inertia force of the thin beam can be used to equivalently describe that of the thick beam segment. The relationship of the force and deflections in both longitudinal and lateral directions at connected points between adjacent beam segments is formulated with continuity conditions. The frequency equation is then established subjected to two both boundary and continuity conditions. Solving the frequency equation yields the natural frequencies of the U-shaped beam actuator. The analytical results are compared with the finiteelement simulation results using ANSYS software. A good agreement is observed between analytical and simulation data, and hence the proposed vibration analysis model is verified. This model provides the first insight study on the vibration analysis of U-shaped electrothermal actuators, which is essentially crucial to dynamic system modelling, control, and dimension optimizations.