Free vibrations of an electroelastic body under biasing fields

We present a systematic analysis of the eigenvalue problem associated with free, small-amplitude vibrations superposed on finite biasing fields in an electroelastic body. An abstract formulation is introduced. The operators in the abstract formulation are shown to be self-adjoint, from which a series of fundamental properties of resonant frequencies and modes are proved concisely. A variational formulation and a perturbation analysis of the eigenvalue problem also are given based on the abstract formulation.