Dynamic electro-thermo-mechanical modeling of a U-shaped electrothermal actuator

In this paper, we develop original analytical electro-thermal and thermo-mechanical models for the U-shaped electro-thermal actuator. The dynamics of the temperature distribution and displacement are obtained as a direct relationship between the system's dimensions, material properties and electrical input. The electro-thermal model provides an exact solution of the hybrid partial differential equations that describe the electro-thermal behaviour for each of the actuator's three connected arms. The solution is obtained using a new calculation method that allows the representation of an integrable function by a hybrid infinite sum of sine and cosine functions. The displacement at the actuator's tip is then calculated using a quasi-static model based on the superposition and virtual works principles. The obtained temperature and displacement solutions are then discussed and compared with finite element method simulations via ANSYS® and experimental results. Comparisons showed good agreement making the proposed modelling a reliable alternative which paves the way for improving the design and optimising the dimensions of U-shaped micro-actuators.