A simple distributed parameter analytical model of multi-layer piezoelectric actuators

Multi-layer piezoelectric actuators (PEAs) are commonly to produce extremely small displacements. Dynamic modeling of PEAs, which can be used to analyze or predict their frequency/time-domain behaviors, plays important roles in the design and control of PEA-based mechanisms. This paper provides a rationale that the complex electrical-mechanical coupled behaviors of PEA can be modelled as an equivalent simple solid with two equivalent excitation forces (proportional to the excitation voltage of PEA) that are equal and opposite, acting at two ends of PEA. Such a rationale is demonstrated through the mathematical derivation process, based on the IEEE standard constitutive relations of piezoelectricity. From the derivation process, the underlying assumptions for the equivalent model to be effective are revealed and the relevant constants in equivalent models are correlated to the standard IEEE piezoelectric material properties. The identified underlying assumptions can provide a guideline for designs to use this simple PEA model. The identified correlation between the constants in equivalent models and the standard IEEE piezoelectric materials allows an alternative way to obtain the equivalent constants, if it is not available for experiments to determine them.