Shell theory for vibrations of piezoceramics under a bias

A consistent derivation of the shell theory in invariant form for the dynamic fields superimposed on a static bias of piezoceramics is discussed. The fundamental equations of piezoelectric media under a static bias are expressed by the Euler-Lagrange equations of a unified variational principle. The variational principle is deduced from the principle of virtual work by augmenting it through Friedrich´s transformation. A set of two-dimensional (2-D), approximate equations of thin elastic piezoceramics is systematically derived by means of the variational principle together with a linear representation of field variables in the thickness coordinate. The 2-D electroelastic equations accounting for the influence of mechanical biasing stress accommodate all the types of incremental motions of a polarized ceramic shell coated with very thin electrodes. Emphasis is placed on the special motions, geometry, and material of the piezoceramic shell. The uniqueness of the solutions to the linearized electroelastic equations of the piezoceramic shell is established by the sufficient boundary and initial conditions.<>