Toward design of Functionally Graded Piezoelectric Ultrasonic Motors using topology optimization

In this work, piezoelectric ultrasonic motors are designed based on the Functionally Graded Material (FGM) concept by using topology optimization. FGMs are composite advanced materials, which are made by changing gradually the properties with position inside material domain. The FGM concept applied to piezoelectric structures allows modifying their dynamic characteristics. In this work, Functionally Graded Piezoelectric Ultrasonic Motors (FGPUMs) are designed, aiming to find the optimal topology and gradation of the material properties along a specific direction to target desired eigenmode shapes. The design of FGPUMs is not an easy task to be accomplished by using trial and error methods; thus, the Topology Optimization Method (TOM) is applied to reach this goal. Here, FGPUMs are designed as standing-wave motors, by combining different vibration modes (different eigenmodes). The eigenmode control is achieved by maximizing the amplitude of vibration at certain user-defined points. The Modal Assurance Criterion is applied as mode shape-tracking method. To treat the material gradation, the Graded Finite Element is implemented. The optimization algorithm is implemented based on Sequential Linear Programming. To show the improvement and the advantage of using FGM and TOM for designing FGPUMs, a graded ultrasonic piezomotor, with material gradation along thickness direction, is considered.