Three-port equivalent circuit of multi-layer piezoelectric stack

Multi-layer piezoelectric transducers (MPS) is a transducer stacked by numerous thin piezo layers, which can used as an actuator, sensor, or energy harvester. This paper points out the limitations of existing equivalent circuits for the effective modelling of MPS and proposes a 3-port equivalent circuit of MPS which is inspired by the idea of network theory and formulated exactly on the basis of the simplified fundamentals. The 3-port equivalent circuit, which separates the MPS into two acoustic ports and one electrical port through an electro-mechanical transformer, offers an exact and explicit representation of electro-mechanical coupled interaction of MPS. It is very straightforward to apply and effectively simplifies and facilitates the analysis, modelling, and calculation of free and loaded vibration of MPS in either transmitter mode (actuator) or receiver mode (sensor or energy harvester). Compared with existing circuit models in literature, the proposed circuit can be extended to any electrical and mechanical condition. Besides, as the proposed circuit elements are explicitly and exactly derived in terms of material and dimension information rather than determined from measured information, the proposed circuit model allows one to predict behaviors with material properties and structural dimension. For validation, a simple case study is carried out. For both free and loaded vibrations of MPS in the case study, the effectiveness of the proposed circuit has been validated by 3D FEA models.