Multimodal and unimodal Functionally Graded Piezoelectric Ultrasonic Transducers

Piezoelectric transducers are usually designed to have a multimodal or unimodal frequency response, which defines the kind of acoustic wave pulse generated (short pulse or continuous wave, respectively). Functionally Graded Materials (FGMs) are made by gradually changing the properties along a material domain. On the other hand, the Topology Optimization Method (TOM) is a generic and systematic optimization technique, which combines optimization algorithms with Finite Element Method to maximize a user-defined objective function. In this work, the main goal is to find the optimal material distribution of Functionally Graded Piezoelectric Ultrasonic Transducers (FGPUTs), including the following requirements: (i) an FGPUT with unimodal dynamic behavior in a desired frequency band; (ii) an FGPUT with multimodal dynamic behavior in a user-defined frequency band. For measuring the strength of a specific mode, the Electromechanical Coupling Coefficient (EMCC) is utilized. For tracking a desirable mode, the Modal Assurance Criterion is applied. The optimization algorithm is constructed based on Sequential Linear Programming. To illustrate the method, two FGPUTs are designed.