Analytical and numerical modelling of deflection of circular three-layer piezoelectric transducer

Abstract

The paper deals with modelling of a circular piezoelectric actuator under electrical loading. A threelayer transducer is analysed. The outer layers of the transducer are made of non-piezoelectric material. The middle layer comprises two elements -a piezoelectric disk, and a ring made of non-piezoelectric material. This design protects the electrical components of the converter against harmful external factors (e.g. hightemperature, chemically active atmosphere). For such a transducer, there is an analytical model describing its deflection as a function of the applied load. Closed-form analytical equations are important tools for predicting and optimizing the operation of devices. However, it should be remembered that analytical models often use various simplifications. Such simplification, in some situations, may cause that the deflection determined with the analytical solution may differ from the actual deflection of the transducer. Therefore, in this paper the results obtained using the analytical model, were compared with the numerical results (no simplifications were used in the numerical simulation). The tests were performed for various constructional variants of the transducer, determined by selected non-dimensional parameters. These parameters include dimensions and mechanical properties of both the piezoelectric disk and passive plates. The obtained results made it possible to determine the degree of applicability of the analytical solution. It was found that the analytical model gives correct results, when the piezoelectric disk is made of various piezoelectric materials (e.g. Lead Zirconate Titanate (PZT), Polyvinylidene Fluoride (PVDF), whereas the passive components are layers made of materials used in MEMS (micro-electro mechanical system), such as silicon, silicon nitride, and most metals. Moreover, the range of relative thicknesses of individual transducer layers was determined, for which the convergence of analytical and numerical solution is obtained.