Dynamic axisymmetric problem of electroelasticity for a rigidly fixed bimorph plate

A nonstationary axisymmetric problem for a circular rigidly fixed bimorph plate consisting of a metal substrate and two piezoelectric elements is studied in this paper. Mechanical vibrations of the structure are made by the action of its end surfaces of electric potential, which is an arbitrary function of the radial coordinate and time. New closed solution is constructed in the framework of electrodynamics in three-dimensional statement by the consistent use of the method of incomplete separation of variables in the form of integral transformations. Consistently Hankel transformation with finite limits on the axial coordinate and generalized finite transformation (FIT) on the radial variable are applied. At each stage of the solution there is a procedure of standardization which allows the appropriate conversion algorithm. The calculated ratio for the components of the displacement vector and the electric field potential allow us to study the variation of the stress-strain state of the bimorph plate. The constructed solution provides an opportunity to make a qualitative and quantitative analysis of connection of electromechanical stress fields in composite laminated electroelastic structures that allow describing the work and finding the geometric characteristics of the typical elements of piezoceramic transducers of resonant and nonresonant classes. Based on the analysis results, it becomes obvious that there is the need for rigidly fixed bimorph systems for excitation of flexural vibrations of the split ring electrodes located on the faces of the piezoceramic plates and for the application of Timoshenko system of equations in applied theory for thin plates taking into account shear deformations. In addition, it became possible to obtain potential change laws, axial-vector components in the tensions and induction of electric field along the thin piezoceramic plate.