Mixed boundary conditions for piezoelectric plates

For plate bending and stretching problems in piezoelectric materials, the reciprocal theorem and the general solution of piezoelasticity are applied in a novel way to obtain the appropriate mixed boundary conditions accurate to all order. A decay analysis technique is used to establish necessary conditions that the prescribed data on the edge of the plate must satisfy in order that it should generate a decaying state within the plate. For the case of axisymmetric bending and stretching of a circular plate, these decaying state conditions are obtained explicitly for the first time when the mixed conditions are imposed on the plate edge. They are then used for the correct formulation of boundary conditions for the interior solution. Supported by the National Natural Science Foundation of China (Grant Nos. 10702077 and 10602001), the Beijing Natural Science Foundation (Grant No. 1083012), and the Alexander von Humboldt Foundation in Germany