Dynamic Problem of Direct Piezoelectric Effect for the Circular Multilayer Plate

The authors consider the dynamic axisymmetric problem for the circular bimorph structure consisting of the metal substrate and the axially polarized piezoceramic plate. Its flexural vibrations are due to mechanical stresses (normal stresses) on the end surface, being an arbitrary function of the radial coordinate and time. The rigid and articulated fixing of the plate cylindrical surface is considered. To solve the problem of the theory of electro elasticity in the three-dimensional formulation, the Hankel finite integral transformations along the axial coordinate and a generalized integral transformation (GIT) in the radial variable are used. The constructed closed solution allows a qualitative and quantitative analyzes of electro-mechanic stress field relatedness in multilayer electro-elastic structures. This makes it possible to describe the work and select all geometric and physical characteristics of typical elements of piezoceramic transducers of resonant and nonresonant classes.