This paper presents a dynamic electro-thermal model for the V- and Z-shaped electrothermal microactuator for the first time. The model predicts the dynamic temperature responses of the actuator operating in vacuum conditions with constant input voltage applied at both ends. Dynamics of the temperature distribution are established, and the exact solution of the hybrid partial differential equation (PDE) is obtained to describe the electro-thermal behavior for each segment of the actuator. To solve the PDE, the final temperature responses are intentionally decomposed into two parts, i.e., the steady-state and transient responses. In addition to the initial and boundary conditions, continuity conditions that describe the temperature and heat flux density between adjacent segments of the actuator are employed to solve the hybrid PDE. The validation of the model is conducted by finite-element simulations using ANSYS software (version 14.0). The analytical results based on the proposed model well agree with the numerical results with ANSYS analysis in terms of predictions on both steady-state and transient responses. Along with the line-shaped beam model, this proposed model serves as the first sub-model in establishing the complete dynamic electro-thermal-mechanical model for the V- and Z-shaped actuators. The developed modeling method paves the way in improving the design and optimizing the dimensions of the actuator in achieving better static and dynamic performances.
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