THE SELECTION OF GEOMETRIC CHARACTERISTICS FOR CIRCULAR MULTI-LAYERED PIEZOELECTRIC PLATES

Abstract

Objectives. For the most efficient conversion of electrical energy into mechanical vibrations, there is a need for an in-depth analysis of the connectivity of physical fields of different nature in multilayer structures.Method. The solution is carried out by the method of finite integral transforms, using successively the Fourier – Bessel transform along the radial coordinate and the generalized transform along the axial variable. In this case, each time the standardization procedure is preliminarily performed (reduction of the boundary conditions to a form, which allows to apply the corresponding transformation).Result. A mathematical model for the calculation of bimorphic plates is developed. Multi-layer solid rigid and hinged structures are considered, in which the principle of reverse piezoelectric effect is used. Closed solutions of non-stationary axisymmetric problems of the electroelasticity theory for multilayer structures by the method of finite integral transformations are constructed. Based on the analysis of the numerical results of the calculation, practical recommendations for the design of piezoceramic transducers of resonance and nonresonance classes are presented. An algorithm has been developed for optimizing the operation of the structures under consideration by selecting their geometrical dimensions and the material used, which makes it possible to most effectively convert the applied electrical load into mechanical displacements.Conclusion. The presented results make it possible to clarify the assumptions about the nature of the distribution of the electric field, which should be used when designing bimorph structures of other configurations, which can only be calculated using applied theories for thin plates.

Keywords

• bimorph piezoceramic plate
• nonstationary axisymmetric problem
• finite integral transformations