The task of direct piezoeffect for a bi-morth plate

Abstract

The research focuses on the dynamic axisymmetric task for a round bi-morph structure consisting of a metal support plate and a piezoceramic axially polarized plate. Its bending oscillations are carried out because of the actions of mechanical load (normal stresses) on its end surface, which is an arbitrary time and radial coordinate function. The rigid and hinged support of the plate cylindrical surface is taken into account. The value of the induced field is calculated by determining the potential on the metal support plate. To solve the task of the theory of the elasticity in a three-dimensional model, the authors apply the Hankel finite integral transformations along the axial coordinate and generalized transformation along the radial variable. Besides, at each stage of the study the standardization procedure is carried out. In the first case it is connected with the use of mixed boundary conditions along the radial coordinate to the mixed form, and in the second case heterogeneous boundary conditions are presented as homogenious. The obtained calculation ratios make it possible to determine the optimal thickness of the piezoceramic plate, which allows to make the most effective transformation of the external mechanical effect into an electrical signal. In addition, it is possible to determine changing characteristics of electromagnetic field according to the height of the piezoceramic plate. This principle can be used in the calculation and design of bi-morph systems with graded-varying thickness and rigidity.