Transfer matrix modeling and experimental verification of forked piezoelectric actuators

Piezoelectric actuators with forked substructures are popular in practical applications. However, there is still a lack of effective modeling methods for forked piezoelectric actuators whose essential substructures converge on the same interface. The critical problem is establishing the transfer conditions between the state vectors distributed on the interface for the forked piezoelectric actuators. To ease these issues, the transfer matrix method is adopted to create forked transfer conditions and to achieve the modeling of the forked piezoelectric actuators in this paper. The forked transfer conditions, including the velocity and force relationships at the interface, are first created. The velocity relationships between state vectors are built by the method of relative velocity, and the force components acting on the interface are equilibrant. Then, a piezoelectric actuator with forked substructures is designed, and its electromechanical coupling model is developed as a case study to confirm the created forked transfer condition. Finally, an actuator prototype is manufactured to verify the proposed forked transfer conditions and the correctness of the developed transfer matrix model of the whole system. The computational and measured vibration characteristics, including resonant frequencies and vibration shapes, agree with each other. Results powerfully demonstrate that the forked connection can transform the vibration direction and realize the amplitude amplification. This modeling method can analyze the vibration characteristics of other similar piezoelectric actuators with the forked substructures.