Dynamic electro-thermo-mechanical modelling of a U-shaped electro-thermal 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 (R) 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.