A simplified transfer matrix of multi-layer piezoelectric stack

Multi-layer piezoelectric stack is a transducer stacked by numerous thin piezo layers which can convert an electrical energy into a mechanical energy in transmitter mode (actuators or vibrators) and can also convert a mechanical energy into an electrical energy in receiver mode (sensors and energy harvesters). Modelling vibrations of multi-layer piezoelectric stack plays a key role in design, fabrication and optimization of many multi-layer piezoelectric stack-based applications. In this article, a simplified transfer matrix of multi-layer piezoelectric stack, which considers the whole multi-layer piezoelectric stack to be an equivalent homogenous bulk, is proposed and formulated to model multi-layer piezoelectric stack-based vibration. When compared with a direct analytical method, the proposed transfer matrix greatly facilitates derivation of analytical solutions or direct calculations when multi-layer piezoelectric stack is stacked with other structures. Compared with using the transfer matrix proposed in the literature, which is subjected to individual piezo layer in multi-layer piezoelectric stack, the proposed simplified transfer matrix contributes to a much simpler form of analytical solution and greatly reduces the computational effort. Case studies have been carried out, which validate the effectiveness of the proposed simplified transfer matrix of multi-layer piezoelectric stack in both transmitter mode and receiver mode.