Approximate equations for the flexure of thin,incomplete, piezoelectric bimorphs

Summary In this paper the linear, three-dimensional, piezoelectric equations for a body in equilibrium are reduced to approximate, two-dimensional ones, treating the flexure of thin bimorphs, partly coated by electrodes (incomplete bimorphs). For that purpose two-dimensional equations are derived for piezoelectric plates and for bimorphs with completely coated faces. An assumption about the charge distribution on the inner electrode is given, stating that the charge vanishes on those parts where the outer faces are free of electrodes. This assumption allows the application of the mentioned, approximate equations for plates and bimorphs to the parts of incomplete bimorphs. By stating edge and continuity conditions, the approximate theory ls completed. The solution for a circular, incomplete, piezoceramic bimorph, loaded by a singular force in the centre, is given and compared with experimental results.