Shell theory for vibrations of piezoceramics under a bias

A consistent derivation of shell theory in invariant form for the dynamic fields superposed on a static bias of piezoceramics is described. The fundamental equations of a piezoelectric medium under a linear bias are expressed by the Euler equations of a unified variational principle. A set of two-dimensional, approximate equations of piezoceramics is systematically derived by means of the variational principle together with a series representation for the field quantities. The set of electroelastic equations accounting for the influence of initial stresses accommodates all the types of incremental motions of a polarized ceramic shell coated with conducting thin electrodes. Emphasis is placed on the special motions, geometry, and material of piezoceramic shell. The sufficient conditions are enumerated for the uniqueness of solutions of the linearized electroelastic equations. Attention is given to the effects of nonlinearity and temperature for the incremental dynamic fields